tag:blogger.com,1999:blog-70753233571554706072024-03-19T08:40:16.120+06:00Блог Олега КривошеинаСтихи и цветы,поздравления и сценарии. Школьная математика, подготовка к ЕГЭ и ГИА,тесты, проекты,задачи и решения. Собственные произведения и фотографии моих цветов: георгины и розы.Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.comBlogger1035125tag:blogger.com,1999:blog-7075323357155470607.post-84517601553704362812024-01-12T08:32:00.000+06:002024-01-12T08:32:07.594+06:00Звёздный фейерверк покорен<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguKcNxOmgy2T78HtULmkyBXwWvUDt6ezQEpMK_NDIl9guK-f4VHt1iS6PytXR-BwRYrNcSBzTL4gubdZ7ByAOuowT8gZ1S7xDcKaq_dt8PQZ-GN16MvGLODnBqBX8ozmVKFvWsWr8Woq4rOItImv6kZtd8HZ1zUGVWe5qtXbXIC_nXfWyp0ES7NvBQXtY/s1280/%D0%97%D0%B2%20%D1%84%D0%B5%D0%B9%D0%B5%D1%80%202023%202.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="925" data-original-width="1280" height="231" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEguKcNxOmgy2T78HtULmkyBXwWvUDt6ezQEpMK_NDIl9guK-f4VHt1iS6PytXR-BwRYrNcSBzTL4gubdZ7ByAOuowT8gZ1S7xDcKaq_dt8PQZ-GN16MvGLODnBqBX8ozmVKFvWsWr8Woq4rOItImv6kZtd8HZ1zUGVWe5qtXbXIC_nXfWyp0ES7NvBQXtY/s320/%D0%97%D0%B2%20%D1%84%D0%B5%D0%B9%D0%B5%D1%80%202023%202.jpg" width="320" /></a></div> 29 декабря в
18-00 часов МУК «ЦНКД» в Таврическом прошёл IV финальный тур конкурсного <br />шоу – проекта
«Звёздный фейерверк – 9». В районном конкурсе принимали участие 6 пар. По
итогам всех четырёх туров наибольшее количество голосов по результатам
судейского голосования набрал дуэт: Сергея Гирина и Ирины Литау. Ирина
Александровна Литау выпускница нашей школы, работает в школе и ее дети успешно
учились и учатся в Харламовской школе. Мы гордимся победой Ирины Александровны,
она впервые участвовала в муниципальном масштабном проекте "Звездный
фейерверк - 9". Желаем дальнейших творческих успехов и ярких побед!<span style="font-size: 14.0pt;"></span><p></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-79408385274735279882024-01-05T15:32:00.000+06:002024-01-05T15:32:58.646+06:00Результаты игры<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhahHbYec4lW2RSKowVG15I9qBIUh2ufzZaTh4sLmD6rg-ibTHS0n9QZ9pl24MzkDyRuDjwXf5Ey3u8W16BWF1TqdRSgi1Udhp48L3maTkym_uCMChWyuvCAN8t2DMUMN4L35-LtSKeE_qje4XvuxgdGy53Mf0pr4zV3_DuzrU5R9N8R2LmCyyCaWfwtUg/s364/%D0%96%D0%B8%D0%B2%D0%BE%D0%B5%20%D0%B3%D1%80%D0%B0%D1%84%D1%84%D0%B8%D1%82%D0%B8%204-11-2013.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="364" data-original-width="310" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhahHbYec4lW2RSKowVG15I9qBIUh2ufzZaTh4sLmD6rg-ibTHS0n9QZ9pl24MzkDyRuDjwXf5Ey3u8W16BWF1TqdRSgi1Udhp48L3maTkym_uCMChWyuvCAN8t2DMUMN4L35-LtSKeE_qje4XvuxgdGy53Mf0pr4zV3_DuzrU5R9N8R2LmCyyCaWfwtUg/s320/%D0%96%D0%B8%D0%B2%D0%BE%D0%B5%20%D0%B3%D1%80%D0%B0%D1%84%D1%84%D0%B8%D1%82%D0%B8%204-11-2013.png" width="273" /></a></div><span style="font-size: medium;">Результаты игры "В физике все интересно" от 5 января 2024 года. <br /><br /></span><p></p><p><span style="font-size: medium;"><b>Среди обучающихся 7 классов</b>: <span style="font-weight: normal;"> <br /></span></span></p>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">Победители:</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">1 место, Бекенев Владимир, ОУ «Сосновская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">2 место Темертасов Диас, ОУ «Весёлорощинская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">3 место Чайбук Артем, ОУ «Карповская
школа»</span></span></h3><h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;"> </span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;">Среди обучающихся 8 классов:</span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">Победители:</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">1 место, Логунов Илья, ОУ «Пристанская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">1 место, Трифонова София, ОУ «Пристанская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">2 место, Рудейко Михаил, ОУ «Пристанская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">3 место Гавриш Богдан, ОУ «Сосновская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">3 место Бородихин Иван, ОУ «Сосновская
школа»</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">3 место Язовский Данил, ОУ «Сосновская
школа»</span></span></h3><h3 style="margin-bottom: .0001pt; margin: 0cm;"><!--[if gte mso 9]><xml>
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</h3><h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">Выражаем благодарность учителям,
подготовившим участников:</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;">Редько Наталье Михайловне, ОУ
"Весёлорощинская школа", Цихач Людмиле Александровне, ОУ Сосновская
школа, Глимановой Хазире Батталовне, ОУ "Пристанская школа", Холявко
Наталье Алексеевне, ОУ "Карповская школа".</span></span></h3>
<h3 style="margin-bottom: .0001pt; margin: 0cm;"><span style="font-size: medium;"><span style="font-weight: normal;"> Наградные материалы будут высланы на электронные почты школ 8 января 2024 г.<br /></span></span></h3>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-4349593703657492102024-01-05T08:26:00.004+06:002024-01-05T09:58:47.723+06:00Задания игры<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivjlTtwCTRDmS9yl6sQt5pLY4NG1Du8K63dq7DmLkKAuqVARXPCXNoyjMkgzLzX63ZeieD0Bgtud5jeSgGN1IvzHt3x3-agUtS6HkmkqdUzmDMtDG7ARhoWtUPnJb-Aayf7thf9NTc_COKtNCm-1QXoyiGdQuMyptSyCMQUIVH-Lkp4kNXbilBgqw5IGM/s1505/%D1%86%D0%B8%D1%84%D0%B8%D1%80%D0%B8%D0%BD%D0%BA%D0%B0%20001.jpg" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" data-original-height="1505" data-original-width="1032" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivjlTtwCTRDmS9yl6sQt5pLY4NG1Du8K63dq7DmLkKAuqVARXPCXNoyjMkgzLzX63ZeieD0Bgtud5jeSgGN1IvzHt3x3-agUtS6HkmkqdUzmDMtDG7ARhoWtUPnJb-Aayf7thf9NTc_COKtNCm-1QXoyiGdQuMyptSyCMQUIVH-Lkp4kNXbilBgqw5IGM/s320/%D1%86%D0%B8%D1%84%D0%B8%D1%80%D0%B8%D0%BD%D0%BA%D0%B0%20001.jpg" width="219" /></a></div><p> <!--[if gte mso 9]><xml>
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7-х классов <br />общеобразовательных учреждений Таврического муниципального района будут опубликованы здесь в 5 января 2024 года 10-00. Ответы принимаются до 10-45.</span></p><p><!--[if gte mso 9]><xml>
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</p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-indent: 1.0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">Уважаемые
участники игры, вам предлагается две формы «Атмосфера» и «Физические явления»,
в которых приведены соответствующие тексты. Тексты надо внимательно прочитать и
ответить на пять последующих вопросов. Максимальное количество баллов, которое
можно получить, ответив на все вопросы в двух формах – 10.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-indent: 1.0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">Форма
с текстом и вопросами «Атмосфера»:</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-indent: 1.0cm;"><a href="https://docs.google.com/forms/d/e/1FAIpQLSc_yEP69knrk1Z4MI9moXOaMZ7yemETkphjoOEq1MlLtAoU9w/viewform"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">https://docs.google.com/forms/d/e/1FAIpQLSc_yEP69knrk1Z4MI9moXOaMZ7yemETkphjoOEq1MlLtAoU9w/viewform</span></a><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;"> </span></p>
<span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%; mso-ansi-language: RU; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;">Форма с текстом и
вопросами «Физические явления»: </span><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 107%; mso-ansi-language: RU; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><a href="https://docs.google.com/forms/d/e/1FAIpQLSfBtBGjrqgF56RyW45WkOGTePo5L-k521NLaI7B4H4jK5bp3w/viewform"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; line-height: 107%;">https://docs.google.com/forms/d/e/1FAIpQLSfBtBGjrqgF56RyW45WkOGTePo5L-k521NLaI7B4H4jK5bp3w/viewform</span></a></span><p></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-68030717003109417952024-01-03T09:25:00.003+06:002024-01-03T18:05:38.348+06:00В физике все интересно<p style="text-align: center;"> <span style="font-family: "Times New Roman","serif"; font-size: 14pt;">ПОЛОЖЕНИЕ <br /></span></p><p><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">
о муниципальной игре «<span style="color: black; mso-bidi-font-weight: bold;">В
физике все интересно</span>» для обучающихся 7 классов общеобразовательных
учреждений Таврического муниципального района Омской области</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18pt;"><a name="bookmark0"><span style="font-size: 14pt; mso-bidi-font-weight: bold;">I.
</span></a><span style="mso-bookmark: bookmark0;"><span style="font-size: 14pt;">Общие
положения</span></span><span style="font-size: 14pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14pt; mso-fareast-font-family: Symbol;">1. </span><span style="font-size: 14pt;">Настоящее Положение определяет порядок организации и проведения
муниципальной игре для обучающихся общеобразовательных учреждений Таврического
муниципального района Омской области «<span style="color: black; mso-bidi-font-weight: bold;">В физике все интересно</span>» (далее игра).</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14pt; mso-fareast-font-family: Symbol;">2. </span><span style="font-size: 14pt;">Основными целями игры являются выявление и развитие интеллектуальных
способностей обучающихся, развитие их коммуникативной компетентности.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">Организаторами игры являются
учителя ОУ «Харламовская школа».</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14pt; mso-fareast-font-family: Symbol;">3. </span><span style="font-size: 14pt;">Для организации и подведения итогов создаются
оргкомитет и жюри.</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18pt;"><a name="bookmark1"><span style="font-size: 14pt; mso-bidi-font-weight: bold;">II. </span></a><span style="mso-bookmark: bookmark1;"><span style="font-size: 14pt;">Участники игры</span></span><span style="font-size: 14pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">1. Участниками игры являются
обучающиеся 7-х классов общеобразовательных учреждений Таврического
муниципального района.</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18pt;"><a name="bookmark2"><span style="font-size: 14pt; mso-bidi-font-weight: bold;">III. </span></a><span style="mso-bookmark: bookmark2;"><span style="font-size: 14pt;">Порядок
организации и проведения игры</span></span><span style="font-size: 14pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">1. Игра проводится в форме тестирования
в дистанционной форме 5 января 2024 г. в <b style="mso-bidi-font-weight: normal;">10.00
ч. До 10.45.</b></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">Регистрация
участников игры производится на основании индивидуальных заявок от участников </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">Ссылка на регистрацию:</span></b><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> </span><a href="https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0"><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0</span></a><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> </span><b><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">до 5 января 2024
года.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">
</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> <b style="mso-bidi-font-weight: normal;">Формы с заданиями будут доступны на сайте
«Блог Олега Кривошеина» </b></span><b><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">5 января </span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">с
10-00 часов. </span></b><a name="more"></a><span style="color: red; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"><a href="http://krivoleg.blogspot.com/">http://krivoleg.blogspot.com/</a></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">Ответы принимаются до 10-45.</span></b><span style="color: red; font-size: 14pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-fareast-language: EN-US; mso-font-kerning: 1.0pt;"></span></p>
<p align="center" class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: center;"><a name="bookmark3"><span style="font-size: 14pt; mso-bidi-font-weight: bold;">IV.</span></a><span style="mso-bookmark: bookmark3;"><span style="font-size: 14pt;">Организационно-методическое обеспечение игры</span></span><span style="font-size: 14pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><span style="font-size: 14pt;">1. Общее руководство проведением игры и ее
организационно-методическое обеспечение осуществляют учителя ОУ «Харламовская
школа»:</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">определяют порядок, сроки и место проведения игры;</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">определяют продолжительность этапов игры;</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">разрабатывают
задания игры на основе примерной основной образовательной программы основного
общего образования;</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">разрабатывает критерии оценивания заданий игры;</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">принимают
заявки на участие в игре от участников;</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 7.1pt; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14pt;">обобщают и анализируют итоги игры.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">2. Состав жюри формируется
из числа учителей математики ОУ «Харламовская школа». Жюри определяет
победителей и призеров на основе рейтинга и распределяет призовые места.</span></p>
<p class="1" style="margin-bottom: 0cm; margin-left: 14.2pt; margin-right: 0cm; margin-top: 0cm; margin: 0cm 0cm 0cm 14.2pt; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;"> </span></p>
<p align="center" class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18pt;"><span style="font-size: 14pt; mso-bidi-font-weight: bold;"> V. </span><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14pt;">Подведение
итогов игры и награждение победителей и призеров</span></b><span style="font-size: 14pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">1. По итогам игры
определяются победители и призеры.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">2. Победители и призеры
определяются по сумме баллов, набранных каждым участником на всех этапах.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14pt;">3. Победители и призеры
награждаются дипломами ОУ «Харламовская школа» Таврического муниципального
района Омской области.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><span style="color: red; font-size: 14pt;"> </span><span style="font-size: 14pt;">
<span style="mso-bidi-font-weight: bold;">Состав жюри </span>муниципальной
онлайн-игры «<span style="color: black; mso-bidi-font-weight: bold;">В физике все
интересно</span>»</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; margin-left: 0cm; margin-right: -.1pt; margin-top: 0cm; margin: 0cm -0.1pt 0cm 0cm; punctuation-wrap: simple; tab-stops: 36.0pt list 54.0pt left 467.7pt; text-autospace: ideograph-numeric;"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 14pt; letter-spacing: 1.5pt;">1)</span><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">Кривошеин
Олег Викторович, учитель </span><span style="font-family: "Times New Roman","serif"; font-size: 14pt; mso-bidi-font-weight: bold; mso-fareast-font-family: FNTSBS+Constantia-Italic;">ОУ
«Харламовская школа».</span><span style="font-family: "Times New Roman","serif"; font-size: 14pt;"></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b><span style="color: black; font-family: "Times New Roman","serif"; font-size: 14pt;"> Заявка на участие в тестировании «В физике все интересно» для
обучающихся 7 классов 5.01.2024 г. Время проведения с 10-00 до 10-45.</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 14pt;"></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><a href="https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0"><span style="font-family: "Times New Roman","serif"; font-size: 14pt;">https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0</span></a><span style="font-family: "Times New Roman","serif"; font-size: 14pt;"> </span></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-34766229063692335832023-11-26T19:52:00.001+06:002023-11-26T19:52:26.338+06:00Положение «В физике все интересно»<p style="text-align: center;"> <span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">ПОЛОЖЕНИЕ <br /></span></p><p><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">
о муниципальной игре «<span style="color: black; mso-bidi-font-weight: bold;">В
физике все интересно</span>» для обучающихся 7 классов общеобразовательных
учреждений Таврического муниципального района Омской области</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18.0pt;"><a name="bookmark0"><span style="font-size: 14.0pt; mso-bidi-font-weight: bold;">I.
</span></a><span style="mso-bookmark: bookmark0;"><span style="font-size: 14.0pt;">Общие
положения</span></span><span style="font-size: 14.0pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14.0pt; mso-fareast-font-family: Symbol;">1. </span><span style="font-size: 14.0pt;">Настоящее Положение определяет порядок организации и проведения
муниципальной игре для обучающихся общеобразовательных учреждений Таврического
муниципального района Омской области «<span style="color: black; mso-bidi-font-weight: bold;">В физике все интересно</span>» (далее игра).</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14.0pt; mso-fareast-font-family: Symbol;">2. </span><span style="font-size: 14.0pt;">Основными целями игры являются выявление и развитие интеллектуальных
способностей обучающихся, развитие их коммуникативной компетентности.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">Организаторами игры являются
учителя ОУ «Харламовская школа».</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: justify;"><span style="color: black; font-size: 14.0pt; mso-fareast-font-family: Symbol;">3. </span><span style="font-size: 14.0pt;">Для организации и подведения итогов создаются
оргкомитет и жюри.</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18.0pt;"><a name="bookmark1"><span style="font-size: 14.0pt; mso-bidi-font-weight: bold;">II. </span></a><span style="mso-bookmark: bookmark1;"><span style="font-size: 14.0pt;">Участники игры</span></span><span style="font-size: 14.0pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">1. Участниками игры являются
обучающиеся 7-х классов общеобразовательных учреждений Таврического
муниципального района.</span></p>
<p align="center" class="10" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18.0pt;"><a name="bookmark2"><span style="font-size: 14.0pt; mso-bidi-font-weight: bold;">III. </span></a><span style="mso-bookmark: bookmark2;"><span style="font-size: 14.0pt;">Порядок
организации и проведения игры</span></span><span style="font-size: 14.0pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">1. Игра проводится в форме тестирования
в дистанционной форме 28 ноября 2023 г. в <b style="mso-bidi-font-weight: normal;">14.00
ч. До 14.45.</b></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">Регистрация
участников игры производится на основании индивидуальных заявок от участников </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">Ссылка на регистрацию:</span></b><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;"><a href="https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0">https://docs.google.com/spreadsheets/d/1JYvfPYzRAbF7SOtbkTuajxukbsHQ_ltUnE5nDhVGR74/edit#gid=0</a></span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> </span><b><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">до 28 ноября
2023 года.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">
</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"> <b style="mso-bidi-font-weight: normal;">Формы с заданиями будут доступны на сайте
«Блог Олега Кривошеина» </b></span><b><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">28 ноября </span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">с
14-00 часов. </span></b><a name="more"></a><span style="color: red; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;"><a href="http://krivoleg.blogspot.com/">http://krivoleg.blogspot.com/</a></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-font-kerning: 1.0pt;">Ответы принимаются до
14-45.<span></span></span></b></p><a name='more'></a><span style="color: red; font-size: 14.0pt; mso-bidi-language: HI; mso-fareast-font-family: NSimSun; mso-fareast-language: EN-US; mso-font-kerning: 1.0pt;"></span><p></p>
<p align="center" class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: center;"><a name="bookmark3"><span style="font-size: 14.0pt; mso-bidi-font-weight: bold;">IV.</span></a><span style="mso-bookmark: bookmark3;"><span style="font-size: 14.0pt;">Организационно-методическое обеспечение игры</span></span><span style="font-size: 14.0pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><span style="font-size: 14.0pt;">1. Общее руководство проведением игры и ее
организационно-методическое обеспечение осуществляют учителя ОУ «Харламовская
школа»:</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">определяют порядок, сроки и место проведения игры;</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">определяют продолжительность этапов игры;</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">разрабатывают
задания игры на основе примерной основной образовательной программы основного
общего образования;</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">разрабатывает критерии оценивания заданий игры;</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">принимают
заявки на участие в игре от участников;</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 7.1pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-indent: 7.1pt;"><span style="color: black; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: Symbol;">· </span><span style="font-size: 14.0pt;">обобщают и анализируют итоги игры.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">2. Состав жюри формируется
из числа учителей математики ОУ «Харламовская школа». Жюри определяет
победителей и призеров на основе рейтинга и распределяет призовые места.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 14.2pt; margin-right: 0cm; margin-top: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;"> </span></p>
<p align="center" class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; tab-stops: list 0cm; text-align: center; text-indent: -18.0pt;"><span style="font-size: 14.0pt; mso-bidi-font-weight: bold;"> V. </span><b style="mso-bidi-font-weight: normal;"><span style="font-size: 14.0pt;">Подведение
итогов игры и награждение победителей и призеров</span></b><span style="font-size: 14.0pt;"></span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">1. По итогам игры
определяются победители и призеры.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">2. Победители и призеры
определяются по сумме баллов, набранных каждым участником на всех этапах.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none; text-align: justify;"><span style="font-size: 14.0pt;">3. Победители и призеры
награждаются дипломами ОУ «Харламовская школа» Таврического муниципального
района Омской области.</span></p>
<p class="1" style="margin-bottom: .0001pt; margin: 0cm; mso-hyphenate: none;"><span style="color: red; font-size: 14.0pt;"> </span><span style="font-size: 14.0pt;">
<span style="mso-bidi-font-weight: bold;">Состав жюри </span>муниципальной онлайн-игры
«<span style="color: black; mso-bidi-font-weight: bold;">В физике все интересно</span>»</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 0cm; margin-right: -.1pt; margin-top: 0cm; punctuation-wrap: simple; tab-stops: 36.0pt list 54.0pt left 467.7pt; text-autospace: ideograph-numeric;"><span style="color: black; font-family: "Times New Roman","serif"; font-size: 14.0pt; letter-spacing: 1.5pt;">1)</span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;">Кривошеин
Олег Викторович, учитель </span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: FNTSBS+Constantia-Italic;">ОУ
«Харламовская школа».</span><span style="font-family: "Times New Roman","serif"; font-size: 14.0pt;"></span></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com1tag:blogger.com,1999:blog-7075323357155470607.post-4561448809702245742022-12-18T11:58:00.007+06:002022-12-18T11:58:52.849+06:00До меньшего основания трапеции<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPutFsFDeF0myMko6vCOty9RHE5OlWG7fa83c7QqsWWKAf7une9EylqRNzvJW-QZWK9EvE1Q9nPuylg35VgJEl006Tby38oVAwa9PGoX1a9ajpODg5AmIl7aaD1B3d9r-zjevacUUe09pMwU8B3fVMJ8we83BdUhtbNh0QhjDBrsymcCvQamufTmN2/s453/%D0%A2%D1%80%D0%B0%D0%BF%202.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="351" data-original-width="453" height="248" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPutFsFDeF0myMko6vCOty9RHE5OlWG7fa83c7QqsWWKAf7une9EylqRNzvJW-QZWK9EvE1Q9nPuylg35VgJEl006Tby38oVAwa9PGoX1a9ajpODg5AmIl7aaD1B3d9r-zjevacUUe09pMwU8B3fVMJ8we83BdUhtbNh0QhjDBrsymcCvQamufTmN2/s320/%D0%A2%D1%80%D0%B0%D0%BF%202.png" width="320" /></a></div><!--[if !mso]>
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<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" Priority="39" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="35" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="10" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="1" SemiHidden="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="11" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="22" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" SemiHidden="true" UnhideWhenUsed="true"
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<w:LsdException Locked="false" Priority="39" Name="Table Grid"/>
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<w:LsdException Locked="false" Priority="61" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1"/>
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<w:LsdException Locked="false" Priority="65" Name="Medium List 1"/>
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<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1"/>
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<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 1"/>
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<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" SemiHidden="true" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" QFormat="true"
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<w:LsdException Locked="false" Priority="29" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" QFormat="true"
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 1"/>
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<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 2"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 3"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 3"/>
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<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 4"/>
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<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 4"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 4"/>
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<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 5"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 5"/>
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<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 5"/>
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<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 5"/>
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<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 5"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 5"/>
<w:LsdException Locked="false" Priority="60" Name="Light Shading Accent 6"/>
<w:LsdException Locked="false" Priority="61" Name="Light List Accent 6"/>
<w:LsdException Locked="false" Priority="62" Name="Light Grid Accent 6"/>
<w:LsdException Locked="false" Priority="63" Name="Medium Shading 1 Accent 6"/>
<w:LsdException Locked="false" Priority="64" Name="Medium Shading 2 Accent 6"/>
<w:LsdException Locked="false" Priority="65" Name="Medium List 1 Accent 6"/>
<w:LsdException Locked="false" Priority="66" Name="Medium List 2 Accent 6"/>
<w:LsdException Locked="false" Priority="67" Name="Medium Grid 1 Accent 6"/>
<w:LsdException Locked="false" Priority="68" Name="Medium Grid 2 Accent 6"/>
<w:LsdException Locked="false" Priority="69" Name="Medium Grid 3 Accent 6"/>
<w:LsdException Locked="false" Priority="70" Name="Dark List Accent 6"/>
<w:LsdException Locked="false" Priority="71" Name="Colorful Shading Accent 6"/>
<w:LsdException Locked="false" Priority="72" Name="Colorful List Accent 6"/>
<w:LsdException Locked="false" Priority="73" Name="Colorful Grid Accent 6"/>
<w:LsdException Locked="false" Priority="19" QFormat="true"
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<w:LsdException Locked="false" Priority="21" QFormat="true"
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<w:LsdException Locked="false" Priority="31" QFormat="true"
Name="Subtle Reference"/>
<w:LsdException Locked="false" Priority="32" QFormat="true"
Name="Intense Reference"/>
<w:LsdException Locked="false" Priority="33" QFormat="true" Name="Book Title"/>
<w:LsdException Locked="false" Priority="37" SemiHidden="true"
UnhideWhenUsed="true" Name="Bibliography"/>
<w:LsdException Locked="false" Priority="39" SemiHidden="true"
UnhideWhenUsed="true" QFormat="true" Name="TOC Heading"/>
<w:LsdException Locked="false" Priority="41" Name="Plain Table 1"/>
<w:LsdException Locked="false" Priority="42" Name="Plain Table 2"/>
<w:LsdException Locked="false" Priority="43" Name="Plain Table 3"/>
<w:LsdException Locked="false" Priority="44" Name="Plain Table 4"/>
<w:LsdException Locked="false" Priority="45" Name="Plain Table 5"/>
<w:LsdException Locked="false" Priority="40" Name="Grid Table Light"/>
<w:LsdException Locked="false" Priority="46" Name="Grid Table 1 Light"/>
<w:LsdException Locked="false" Priority="47" Name="Grid Table 2"/>
<w:LsdException Locked="false" Priority="48" Name="Grid Table 3"/>
<w:LsdException Locked="false" Priority="49" Name="Grid Table 4"/>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Из
сборника «ОГЭ 2023.Математика. 50 вариантов. Типовые варианты экзаменационных
заданий от разработчиков ОГЭ» под редакцией И.В. Ященко.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Вариант
8. Задание 25.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
равнобедренную трапецию, периметр которой равен 80, а площадь равна 320, можно
вписать окружность. Найдите расстояние от точки пересечения диагоналей трапеции
до её меньшего основания.</span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Решение. <br /></span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Если
в четырехугольник можно вписать окружность, то суммы его противоположных сторон
равны. Значит АВ+С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=ВС+А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=40. Так как трапеция равнобедренная, то АВ=С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=20. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Площадь
трапеции рана произведению полусуммы оснований на высоту, то </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">320=0,5*(
ВС+А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">)*СН, отсюда 320=0,5*40*СН, СН=16.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">СН,
ВЕ и КР – высоты трапеции, КР проходит через точку пересечения диагоналей О.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Треугольники
АВЕ и СН</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равны, так как они прямоугольные, равны катеты ВЕ и
СН, гипотенузы АВ и С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.<span></span></span></p><a name='more'></a><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Из
равенства треугольников АВЕ и СН</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> следует АЕ=Н</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">. По теореме Пифагора катет Н</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен квадратному корню из 20*20-16*16 = 144. Н</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=12. Отсюда ВС=(40-2*12)/2 = 8. Значит А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> = 40 – 8 =32.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Далее,
треугольники ОВС и ОА</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> подобны по 1
признаку (углы ВОС и АО</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">– вертикальные,
углы ВСА и СА</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">– накрестлежащие при параллельных ВС и А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и секущей АС). Значит ОС:ОА=ВС: А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=8:32=1:4.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Аналогично
подобны треугольники КОС и РОА, значит КО:ОР=ОС:ОА=1:4.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Значит
КО=СН:5=16:5=3,2.</span></p>
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<p></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-52963334395849413612022-12-18T10:59:00.006+06:002022-12-18T11:20:21.285+06:00Найдите площадь параллелограмма<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPwX7TR-eoGASrAZyGBpy52TqAmQuv-HzDbScjEcIsro9FS4kRTjCYYNBvGipfnAt_QKy1Onb58LZ0DX2LJ0gPHtgjUF3TpLi3rdhkmrM14S9FLyuf6scncnVtYFPaQBnlQfv1QYzk3eh7byH1Ut21ze1m7QpcoH_zrnkPM5DP2teugRD97kPkdCRd/s342/%D0%9F%D0%B0%D1%80%D0%B0%D0%BB%201.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="212" data-original-width="342" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiPwX7TR-eoGASrAZyGBpy52TqAmQuv-HzDbScjEcIsro9FS4kRTjCYYNBvGipfnAt_QKy1Onb58LZ0DX2LJ0gPHtgjUF3TpLi3rdhkmrM14S9FLyuf6scncnVtYFPaQBnlQfv1QYzk3eh7byH1Ut21ze1m7QpcoH_zrnkPM5DP2teugRD97kPkdCRd/s320/%D0%9F%D0%B0%D1%80%D0%B0%D0%BB%201.png" width="320" /></a></div> <!--[if !mso]>
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<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Из
сборника «ОГЭ 2023.Математика. 50 вариантов. Типовые варианты экзаменационных
заданий от разработчиков ОГЭ» под редакцией И.В. Ященко.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Вариант 6. Задание 25.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">В
параллелограмме <i>ABCD</i> проведена диагональ <i>AC</i>. Точка <i>O</i>
является центром окружности, вписанной в треугольник <i>ABC</i>. Расстояния от
точки <i>O</i> до точки <i>A</i> и прямых <i>AD</i> и <i>AC</i> соответственно
равны 25, 17 и 7. Найдите площадь параллелограмма <i>ABCD</i>.</span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"> <b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Решение</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. <br /></span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Построим
параллелограмм АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> и окружность,
вписанную в треугольник АВС с центром О. По условию АО=25, ОН=17, ОК=7. Вспомним,
что центр вписанной окружности треугольника - это точка пересечения его биссектрис,
поэтому АО, ВО и ОС – биссектрисы углов ВАС, АВС и ВСА. Радиусы ОК, ОЕ и ОР соответственно
перпендикулярны касательным АС, АВ и ВС.<span></span></span></p><a name='more'></a><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Из
прямоугольного треугольника <span style="mso-bidi-font-style: italic;">AOK</span>
по теореме Пифагора найдём АК. Квадрат АК равен 25*25-7*7=576. АК=24. Так как
отрезки касательных, проведенных к окружности из одной точки равны, то АЕ
+АК=24. Аналогично ВЕ=ВР, СР=СК.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Площадь
треугольника <i>ABC</i> можно найти как половину произведения радиуса вписанной
окружности на периметр. Тогда площадь параллелограмма АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна произведению радиуса ОК на периметр
треугольника АВС. Найдем периметр треугольника АВС, он равен АЕ+ВЕ+ВР+РС+СК+АК
= 24+2ВР+2РС+24= 48+2(ВР+РС)= 48+2ВС.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Значит
площадь параллелограмма АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна
7*(48+2ВС).</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">С
другой стороны площадь параллелограмма равна произведению высоты на основание,
то есть РН*А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">=24А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">=24ВС.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Приравнивая
полученные выражения, получаем уравнение 7*(48+2ВС)=24ВС. Раскроем скобки 336
+14 ВС= 24 ВС, 336 = 10 ВС, ВС = 33,6. Площадь параллелограмма АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна 24*33,6 = 806,4.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Ответ
806,4.</span></p>
<p></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-88032551773565066682022-12-18T09:02:00.002+06:002022-12-18T11:21:02.674+06:00Диагонали и средняя линия трапеции<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7L7HsM7vYP7FJVmepkh7pMDEkQ0kuOxaiBh0zBgGbmWfa35ntD6PoCL5FGjdj58ZIdPZH4eFXbFFANDpxsvJuNupk2Kfz5G6Br2ojwSd66y87buvGaRC-k3Exu9W0hedHOpA4fwHbVxv0xNkwJbvNTCsZvIJ9su3uFkadvjnzJXVew-t-1ylmvQNh/s521/%D0%A2%D1%80%D0%B0%D0%BF%201.png" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="273" data-original-width="521" height="168" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7L7HsM7vYP7FJVmepkh7pMDEkQ0kuOxaiBh0zBgGbmWfa35ntD6PoCL5FGjdj58ZIdPZH4eFXbFFANDpxsvJuNupk2Kfz5G6Br2ojwSd66y87buvGaRC-k3Exu9W0hedHOpA4fwHbVxv0xNkwJbvNTCsZvIJ9su3uFkadvjnzJXVew-t-1ylmvQNh/s320/%D0%A2%D1%80%D0%B0%D0%BF%201.png" width="320" /></a><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Из сборника «ОГЭ
2023.Математика. 50 вариантов. Типовые варианты экзаменационных заданий от
разработчиков ОГЭ» под редакцией И.В. Ященко.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Вариант 7. Задание 25.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Найдите
площадь трапеции, диагонали которой равны 17 и 9, а средняя линия равна 5.</span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Решение.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> Построим
трапецию АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">с основаниями ВС и А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. Из условия АС=17, В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
=9. Так как средняя линия трапеции равна половине суммы оснований, то ВС+А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">=5*2=10. Из вершины С трапеции проведем прямую,
параллельную В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, она пересечет прямую А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
в точке Е. Получили параллелограмм ВСЕ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, у которого ВС=</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Е, В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">=СЕ. Диагональ С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> делит параллелограмм на два равных треугольника ВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> и СЕ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. Значит площадь
трапеции АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна площади треугольника АСЕ, у которого АС=17,
СЕ=9, АЕ = А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Е = А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">+ВС=2*5 = 10.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">По
формуле Герона находим площадь треугольника АСЕ. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Р=(17+9+10)/2
=18. Значит площадь треугольника АСЕ равна корню квадратному из произведения 18(18-17)(18-9)(18-10)
= 18*1*9*8. Значит площадь треугольника АСЕ равна 36.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Ответ
36.</span></p>
<p></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-22947277120005312152022-10-02T22:14:00.000+06:002022-10-02T22:14:07.809+06:00Осенние напевы<iframe width="480" height="270" src="https://youtube.com/embed/m3vk9F543Ls" frameborder="0"></iframe>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-33266667015473808192022-02-16T09:06:00.002+06:002022-02-16T09:06:51.191+06:00 Диагональ разбивает трапецию на два равнобедренных треугольника<p> <!--[if !mso]>
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</p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Рассмотрим
еще одну геометрическую задачу из сборника «ЕГЭ 2022. Математика. Профильный
уровень. 50 вариантов. Типовые варианты экзаменационных заданий от
разработчиков ЕГЭ. Под редакцией И.В. Ященко. – М. Издательство «Экзамен»,
2022. 231 стр.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">16
задания.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Вариант
3. </span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg7YZDclu3X2lKsuRK4wofxp0FusP_h8EM81jq-6La302Oa_4ydMRA28knInaUV6AFqDI942uPAY3Oee5TLqH9LrnzVc7Td7znRgNNIvpwXBCKisMXGaGzO2S1yU5GtCCEOKfGwXTLa1qDRvl_37RSiQvJ6FHEitdVyj9NQnvSp43OS9DCzz9q1ZwVI=s475" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="333" data-original-width="475" height="224" src="https://blogger.googleusercontent.com/img/a/AVvXsEg7YZDclu3X2lKsuRK4wofxp0FusP_h8EM81jq-6La302Oa_4ydMRA28knInaUV6AFqDI942uPAY3Oee5TLqH9LrnzVc7Td7znRgNNIvpwXBCKisMXGaGzO2S1yU5GtCCEOKfGwXTLa1qDRvl_37RSiQvJ6FHEitdVyj9NQnvSp43OS9DCzz9q1ZwVI=s320" width="320" /></a></div><br /><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В трапеции АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> основания </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и ВС. Диагональ
АС разбивает ее на два равнобедренных треугольника с основаниями </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и АВ.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">а)
Докажите, что луч </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В – биссектриса
угла </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">б)
Найдите АВ, если известны длины диагоналей трапеции: В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
= 8 и АС = 5.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Решение.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">а)
По условию в треугольнике АВС ВС=АС, в треугольнике АС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
АС=С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">. Значит ВС=С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.
Отсюда следует, что угол СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен углу С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В. Далее заметим, что угол СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен углу А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
как накрест лежащие при параллельных прямых ВС и А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
и секущей В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">. Следовательно, углы С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
и А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В равны.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">б)
<b style="mso-bidi-font-weight: normal;">Первый способ. Алгебраический.<span></span></b></span></p><a name='more'></a><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Так
как ВС= С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=АС=5. В треугольнике СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
известны все стороны и можно найти его площадь по формуле Герона. Полупериметр
треугольника СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен (5+5+8)/2
= 9. Значит площадь треугольника СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равна корню
квадратному из произведения чисел 9*1*4*4. Площадь треугольника СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равна 12. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С
другой стороны площадь треугольника СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равна 0,5* С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">* В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">*</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">sin</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В,
то есть </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">0,5*
С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">* В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">*</span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">sin</span></i><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В = 12, подставляя длины сторон, получаем</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">0,5*5*8*<i style="mso-bidi-font-style: normal;"> </i></span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">sin</span></i><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
= 12, отсюда </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">sin</span></i><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В = 0,6. Используя основное тригонометрическое
тождество, находим </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">cos</span></i><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
= 0,8. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">По
формуле косинуса двойного угла находим, что </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">cos</span></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А = 0,28. Далее мы знаем, что угол С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А равен углу СА</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">,
а угол СА</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен углу ВСА (накрест лежащие при параллельных А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и ВС и секущей АС). Значит </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">cos</span></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">ВСА = 0,28. Теперь мы можем применить
теорему косинусов для нахождения стороны АВ. Квадрат стороны АВ равен
5*5+5*5-2*5*5*<i style="mso-bidi-font-style: normal;"> </i>0,28 = 36. Значит АВ =
6.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">б) <b style="mso-bidi-font-weight: normal;">Второй способ. Геометрический. </b></span></p><div class="separator" style="clear: both; text-align: center;"><b style="mso-bidi-font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEh6Suy26exFbK4unGaMqDwDW-HWa6eOxBa_af07xC5HIcIkF_mXVA6_S8ImZj_fOSccURLP81uV3Tk-ZhaUXLtEHKYFyu45F7XlTPp12VAUoNsJIzEbJwRoYGkQUYW5BIKUhp_WLBQAav1mTJ7YJL0rkQc7NEGZx7NxKgkDpRNkvRish8HmYTA17mF_=s569" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="333" data-original-width="569" height="187" src="https://blogger.googleusercontent.com/img/a/AVvXsEh6Suy26exFbK4unGaMqDwDW-HWa6eOxBa_af07xC5HIcIkF_mXVA6_S8ImZj_fOSccURLP81uV3Tk-ZhaUXLtEHKYFyu45F7XlTPp12VAUoNsJIzEbJwRoYGkQUYW5BIKUhp_WLBQAav1mTJ7YJL0rkQc7NEGZx7NxKgkDpRNkvRish8HmYTA17mF_=s320" width="320" /></a></b></div><b style="mso-bidi-font-weight: normal;"><br /></b><p></p><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Проведем
через вершину В прямую, параллельную диагонали АС, точку пересечения этой
прямой с продолжением стороны А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">обозначим буквой
К. В результате мы получили параллелограмм КВСА. Так как ВС=АС=5, то КВСА –
ромб. Диагональ АС ромба КВСА делит угол ВСА на два равных, а так как угол ВСА
равен углу САВ и равен углу С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А, то угол ВСК
равен углу С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В. Легко заметить, что треугольники КВС и ВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">равны (у них углы ВСК, ВКС, С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А, СА</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равны, а значит
равны и углы КВС и ВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">, стороны КВ, ВС
и С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> тоже равны) по первому признаку равенства
треугольников. Значит СК= В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">=8.</span>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Так
как диагонали ромба перпендикулярны и точкой пересечения делятся пополам, то
КО=ОС=4, ВО=ОА. В прямоугольном треугольнике ОВС гипотенуза ВС=5, катет ОС=4,
по теореме Пифагора находим, что ВО=3. Значит АВ=6.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Второй
способ проще, но надо увидеть дополнительное построение.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Задание для самостоятельного решения.</span></b></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Вариант
4.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В
трапеции АВС</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> основания </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и ВС. Диагональ
АС разбивает ее на два равнобедренных треугольника с основаниями </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и АВ.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А)
Докажите, что луч </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В – биссектриса
угла </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Б)
Найдите АВ, если известны длины диагоналей трапеции: В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
= 12 и АС = 7,5.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><strong>Для решения задачи первым
способом необходимо помнить: </strong></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><strong>Теорема косинусов</strong>
звучит так: квадрат стороны треугольника равен сумме квадратов двух других его сторон
минус удвоенное произведение этих сторон на косинус угла между ними.</p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><strong>Формула теоремы косинусов:</strong></p>
<p style="margin-bottom: .0001pt; margin: 0cm;"><i>a<sup>2</sup> = b<sup>2</sup> +
c<sup>2</sup> - 2bc cos α</i></p><p style="margin-bottom: .0001pt; margin: 0cm;"><i></i></p><div class="separator" style="clear: both; text-align: center;"><i><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgOS1gpeJyiXPKO7j06cmap3HXBYqLHcweHDAPXQKCFTwipoMc5A6uwZtXVsaNrYn4tcHednxtt4sqaFxWVfFiLpiYp_6TvixjJBn_KGSWW6d8P57BHns3c8ZawL2bxpgrZwXukYXCk-Sm0u_lUu9jt9xCS-FIbLs9S5fqE-S4k8YCwBKNMq-DRXLOr=s919" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="633" data-original-width="919" height="275" src="https://blogger.googleusercontent.com/img/a/AVvXsEgOS1gpeJyiXPKO7j06cmap3HXBYqLHcweHDAPXQKCFTwipoMc5A6uwZtXVsaNrYn4tcHednxtt4sqaFxWVfFiLpiYp_6TvixjJBn_KGSWW6d8P57BHns3c8ZawL2bxpgrZwXukYXCk-Sm0u_lUu9jt9xCS-FIbLs9S5fqE-S4k8YCwBKNMq-DRXLOr=w400-h275" width="400" /></a></i></div><i><br /> </i><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhX7eEljymAUtW2jMhU9lQAm4ZUb7Bb1JL3MCEoxifMzlXbzMZuOLP34_mnRnQ477AqhqOfgbXv_flVvNsmQaWtVzMw05YfGLyouw4TF9Vr-HMWaq5-QR2RxYa_cqbYZwu_zeZlRsfJ89Olo05tEvD49EuzIn4AHBbnRac8ZqHWgqWFz9DGtYOH6idz=s1554" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1554" data-original-width="1150" height="400" src="https://blogger.googleusercontent.com/img/a/AVvXsEhX7eEljymAUtW2jMhU9lQAm4ZUb7Bb1JL3MCEoxifMzlXbzMZuOLP34_mnRnQ477AqhqOfgbXv_flVvNsmQaWtVzMw05YfGLyouw4TF9Vr-HMWaq5-QR2RxYa_cqbYZwu_zeZlRsfJ89Olo05tEvD49EuzIn4AHBbnRac8ZqHWgqWFz9DGtYOH6idz=w296-h400" width="296" /></a></div><br /><p></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com1tag:blogger.com,1999:blog-7075323357155470607.post-52724560035481628512022-02-16T07:10:00.003+06:002022-02-16T07:13:26.662+06:00На продолжении стороны АС<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEg0d7_zrgTuyMak2ba4lI21Oq6qa9YvXrlGJ0rfbxEua1GkPQlhcyV9pt9-55qsWUEijPfxhb2dra1svVTFMPHSpxAaSgBpM1avYOzGA5f7z9L2g40EX3UjN1gdYlFPRMMRA_E8K1dHfu5Zc4NA8jK2han20fq4-mly2EJ__8eGSsQQxhYoP-dkl6YF=s765" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="332" data-original-width="765" height="139" src="https://blogger.googleusercontent.com/img/a/AVvXsEg0d7_zrgTuyMak2ba4lI21Oq6qa9YvXrlGJ0rfbxEua1GkPQlhcyV9pt9-55qsWUEijPfxhb2dra1svVTFMPHSpxAaSgBpM1avYOzGA5f7z9L2g40EX3UjN1gdYlFPRMMRA_E8K1dHfu5Zc4NA8jK2han20fq4-mly2EJ__8eGSsQQxhYoP-dkl6YF=s320" width="320" /></a><br /><!--[if !mso]>
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</xml><![endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Рассмотрим
геометрическую задачу из сборника «ЕГЭ 2022. Математика. Профильный уровень. 50
вариантов. Типовые варианты экзаменационных заданий от разработчиков ЕГЭ. Под
редакцией И.В. Ященко. – М. Издательство «Экзамен», 2022. 231 стр.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">16 задания</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Вариант
1. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">На
продолжении стороны АС за вершину А треугольника АВС отложили отрезок </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, равный стороне АВ. Прямая, проходящая через точку
А параллельно В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, пересекает
сторону ВС в точке М.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">а)
докажите, что АМ – биссектриса угла ВАС.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">б)
Найдите площадь трапеции </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">A</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">МВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, если площадь треугольника АВС равна 180 и известно
отношение АС:АВ = 3:2. </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Решение.<span></span></span></p><a name='more'></a><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">а)
А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> = АВ по условию, значит в треугольнике АВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> угол </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равен углу АВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. Но угол </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> также равен
углу САМ, как односторонние при параллельных В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
и АМ и секущей АС. Угол АВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равен углу ВАМ,
как накрест лежащие при параллельных В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> и АМ и секущей
АВ. Следовательно, угол ВАМ равен углу САМ.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">б)
Рассмотрим треугольники ВАМ и САМ. Их площади соответственно равны <i style="mso-bidi-font-style: normal;">0,5*АВ*АМ*</i></span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">sin</span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">ВАМ</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> и <i style="mso-bidi-font-style: normal;">0,5*АС*АМ*</i></span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">sin</span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">САМ</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> . Значит
отношение площадей этих треугольников равно <i style="mso-bidi-font-style: normal;">0,5*АВ*АМ*</i></span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">sin</span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">ВАМ </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">: <i style="mso-bidi-font-style: normal;">0,5*АС*АМ*</i></span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">sin</span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">САМ </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">= <i style="mso-bidi-font-style: normal;">АВ</i>
: <i style="mso-bidi-font-style: normal;">АС</i> = 2 : 3. Значит, если площадь
треугольника ВАМ разделить на две равные части, то площадь треугольника САМ
состоит из трех таких частей. Соответственно, площадь треугольника АВС состоит
из 5 таких частей. Отсюда, площадь треугольника САМ равна 180 : 5 * 3 = 108.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Далее
заметим, что треугольники САМ и СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> подобны по
первому признаку ( угол С – общий, угол </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">
равен углу САМ).</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Имеем
АС : С</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> = 3:5, значит отношение площадей треугольников САМ
и СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равно 9:25. Отсюда площадь треугольника СВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна 108:9*25 = 300.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Площадь
трапеции АМВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> равна 300 – 108 = 192.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Ответ
192.</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><!--[if gte mso 9]><xml>
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</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Задача для самостоятельного решения.</span></p><p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Вариант
2.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">На
продолжении стороны АС за вершину А треугольника АВС отложили отрезок </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">, равный стороне АВ. Прямая, проходящая через точку
А параллельно В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">, пересекает
сторону ВС в точке М.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">А)
докажите, что АМ – биссектриса угла ВАС.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Б)
Найдите площадь трапеции </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">A</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">МВ</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">, если площадь треугольника АВС равна 144 и известно
отношение АС:АВ = 3:1.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> </span></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-39457360688192063032022-02-07T20:46:00.006+06:002022-02-07T20:49:11.425+06:00Вова и Гоша решают задачи<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEg5Pt_YJHfJRlQNLmL-peYV8cU_3ynHgLD0s_xWA1mVh1KFd9SbA768aBXZlvh4o1WWJY8_stVFoPdOuIKPd1d1Z_cWDISqU-cij_0sl_bKOY2Fh7tK51T0zuemZLgDMDBBswWlW5KLGbXEWiJ2RIqB_t0spHaNv8OuaxXP_PGAO-HQEkk3_f2a4RWB=s567" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="360" data-original-width="567" height="203" src="https://blogger.googleusercontent.com/img/a/AVvXsEg5Pt_YJHfJRlQNLmL-peYV8cU_3ynHgLD0s_xWA1mVh1KFd9SbA768aBXZlvh4o1WWJY8_stVFoPdOuIKPd1d1Z_cWDISqU-cij_0sl_bKOY2Fh7tK51T0zuemZLgDMDBBswWlW5KLGbXEWiJ2RIqB_t0spHaNv8OuaxXP_PGAO-HQEkk3_f2a4RWB=s320" width="320" /></a></div> При выполнении тестовых заданий у некоторых учащихся возникли затруднения с решением задачи: <br /><br /><p></p><p>
</p><p class="leftmargin" style="margin-bottom: .0001pt; margin: 0cm; text-indent: 1cm;">Вова
и Гоша решают задачи. За час Вова может решить на две задачи больше, чем Гоша
(при этом оба за час решают целое количество задач). Известно, что вместе они
решат 33 задачи на 1 час 15 минут быстрее, чем это сделал бы один Вова. За
какое время Гоша может решить 20 задач? Ответ дайте в часах.</p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Приведем решение.<span></span></span></b></p><a name='more'></a><p></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm; text-indent: 1cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Пусть
Гоша решает за час <i style="mso-bidi-font-style: normal;">х</i> задач, тогда
Вова за час решает <i style="mso-bidi-font-style: normal;">х+2</i> задачи. Вместе
за час решают <i style="mso-bidi-font-style: normal;">2х+2</i> задачи. Значит 33
задачи они вместе решат за <i style="mso-bidi-font-style: normal;">33/(2х+2)</i>
часов, а один Вова за <i style="mso-bidi-font-style: normal;">33/(х+2)</i> часов.
Поскольку вместе ребята решат на 1 час 15 минут (1,25 часа) быстрее, то
получаем уравнение</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">33/(х+2)- 33/(2х+2)=1,25</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">, умножив обе
части уравнения на 4 получаем</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">132/(х+2)- 132/(2х+2)=5</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> или </span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">132/(2х+2) - 132/(х+2)=5(2х+2)(х+2)</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">,</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">264х+264 - 132х-264=10х<sup>2</sup>+20х+10х+20</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">,</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">132х=10х<sup>2</sup>+30х+20</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">,</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">10х<sup>2</sup>-102х+20=0, х<sub>1</sub>=10,
х<sub>2</sub>=0,2. </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Второе
решение не соответствует условию задачи.</span></p>
<p class="MsoNormal" style="line-height: normal; margin-bottom: 0cm;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">20:10=2</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">. Ответ 2.</span></p>
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<![endif]--></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com2tag:blogger.com,1999:blog-7075323357155470607.post-34366939764144408872022-02-06T14:28:00.006+06:002022-02-06T14:28:59.499+06:00Трапеция, вписанная в окружность<p class="MsoNormal"> <b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Рассмотрим
задачу из учебника геометрии 8 класса, решение которой пригодится сдающим ЕГЭ
по математике профильного уровня. </span></b></p><div class="separator" style="clear: both; text-align: center;"><b style="mso-bidi-font-weight: normal;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjj9bUeKsa_Ku1qk4GEmgj3ycLLmSu7A8bGjKsq2TgbOlxp6fIRGt0dEfI1ZGZyZGJmfyLJh5kDsLHKhrEcmVatopV83qNTgj3zrlJfMTUNN4_sFx9fp77jYeOAKryLHfLVQd6FhRmAH7dHSxE_6SS_BIqBQud8JFbRsgNQbwUDocBDRFZt_K6193oE=s517" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="514" data-original-width="517" height="318" src="https://blogger.googleusercontent.com/img/a/AVvXsEjj9bUeKsa_Ku1qk4GEmgj3ycLLmSu7A8bGjKsq2TgbOlxp6fIRGt0dEfI1ZGZyZGJmfyLJh5kDsLHKhrEcmVatopV83qNTgj3zrlJfMTUNN4_sFx9fp77jYeOAKryLHfLVQd6FhRmAH7dHSxE_6SS_BIqBQud8JFbRsgNQbwUDocBDRFZt_K6193oE=s320" width="320" /></a></b></div><b style="mso-bidi-font-weight: normal;"><br /><br /></b><p></p>
<p class="MsoNormal"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Задача.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
Диагональ равнобокой трапеции перпендикулярна боковой стороне, которая равна 12
см. Найдите среднюю линию трапеции, если радиус окружности, описанной около
трапеции, равен 10 см.</span></p>
<p class="MsoNormal"><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Решение.</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
При построении чертежа к задаче необходимо учесть, что если диагональ вписанной
трапеции перпендикулярна боковой стороне, то большее основание является
диаметром описанной окружности (прямой вписанный угол опирается на диаметр). </span></p>
<p class="MsoNormal" style="text-indent: 1.0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Итак, в равнобедренной трапеции
</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">ABCD</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">боковая
сторона АВ = 12 см, диаметр </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">AD</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
= 20 см. Треугольник </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">ABD</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">–
прямоугольный, из вершины прямого угла проведем высоту ВН. Так как квадрат
катета прямоугольного треугольника равен произведению гипотенузы на проекцию
этого катета на гипотенузу. Таким образом АН = АВ*АВ/А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;"> = 12*12/20 = 7,2 см. Тогда средняя
линия трапеции </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">MN</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
= Н</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">
= 20 – 7,2 = 12,8 см.</span></p>
<p class="MsoNormal" style="text-indent: 1.0cm;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Подобные задачи:<span></span></span></p><a name='more'></a><p></p>
<p class="MsoListParagraphCxSpFirst" style="margin-left: 46.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Диагональ
равнобедренной трапеции перпендикулярна боковой стороне. Вычислите радиус
окружности, описанной около трапеции, если длина ее диагонали равна 12 см, а
длина боковой стороны равна 9 см.</span></p>
<p class="MsoListParagraphCxSpMiddle" style="margin-left: 46.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 107%;">Диагональ
равнобедренной трапеции перпендикулярна боковой стороне. Найдите диагональ
трапеции, если радиус описанной окружности равен 13 см, а боковая сторона - 10
см.</span></p>
<p class="MsoListParagraphCxSpLast" style="line-height: normal; margin-left: 46.35pt; mso-add-space: auto; mso-list: l0 level1 lfo1; mso-margin-bottom-alt: auto; mso-margin-top-alt: auto; mso-outline-level: 1; text-indent: -18.0pt;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: RU; mso-font-kerning: 18.0pt;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-bidi-font-weight: bold; mso-fareast-font-family: "Times New Roman"; mso-fareast-language: RU; mso-font-kerning: 18.0pt;">Диагональ равнобокой трапеции перпендикулярна
боковой стороне, а проекция этой диагонали на большее основание равна 10 см.
Боковая сторона трапеции равна 12 см. Найдите высоту и основания трапеции.</span></p>
Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-82699326585196194692022-02-05T10:52:00.002+06:002022-02-05T10:52:35.305+06:00День российской науки<p> <a href="https://blogger.googleusercontent.com/img/a/AVvXsEitT1INl8-ipcDqupUVeMURIJ3p9tfHGsfS38XOX0z6ozRNHRQrhWELoWvSNCQDH5zvirc6tNajqA3FigFj4ERoCZESipi7abO4ZOb0YQOaUrh0UsNDppWqy1vcWcQnEmGsb_yyPpYaOV0Kdz3Dekw1LWwjKCuonT7Dgy7hsA04OC58VStqL5kSB-9j=s128" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="128" data-original-width="128" height="128" src="https://blogger.googleusercontent.com/img/a/AVvXsEitT1INl8-ipcDqupUVeMURIJ3p9tfHGsfS38XOX0z6ozRNHRQrhWELoWvSNCQDH5zvirc6tNajqA3FigFj4ERoCZESipi7abO4ZOb0YQOaUrh0UsNDppWqy1vcWcQnEmGsb_yyPpYaOV0Kdz3Dekw1LWwjKCuonT7Dgy7hsA04OC58VStqL5kSB-9j" width="128" /></a><em>8 февраля отмечается День российской науки. Специально к этому празднику мы подготовили познавательный и нескучный тест. <br /></em></p>
<p>День российской науки — праздник учёных и академиков, преподавателей и
студентов, исследователей, которые посвятили себя сложному и
увлекательному делу — научному познанию. Все помнят Ломоносова и
Менделеева, Павлова и Циолковского и их выдающиеся достижения, но не все
знают, что наши современники совершают не менее значимые открытия и
прорывы в науке. Вот только некоторые из них.</p>
<ul style="margin-left: 40px;"><li>С 2000 по 2010 год физики из лаборатории имени Флёрова в
Объединённом институте ядерных исследований в Дубне впервые
синтезировали шесть самых тяжёлых элементов с атомными номерами со 113
по 118. Элемент с атомным номером 115 назван московием. Зачем они нужны?
Юрий Оганесян, научный руководитель лаборатории, объясняет это тем, что
учёные могут разобраться в процессах образования элементов в природе и,
возможно, даже ответить на один из важнейших вопросов науки: где лежит
граница нашего материального мира?</li><li>В нижегородском Институте прикладной физики РАН учёные разработали
один из самых мощных лазерных комплексов в мире — установку PEARL
(PEtawatt pARametric Laser), которая способна выдать световое излучение
мощностью 0,56 петаватт (1 петаватт = 1015 ватт). С помощью такого
лазера можно исследовать экстремальные физические процессы и проводить
термоядерные реакции.</li><li>В 2021 году специалисты Российского квантового центра и Физического
института имени Лебедева РАН создали прототип квантового компьютера на
ионах, применив кудиты — многоуровневые носители информации. В ближайшие
несколько лет учёные планируют создать универсальный квантовый
компьютер с облачным доступом.</li><li>Химики и биологи Уральского федерального университета в
сотрудничестве с учёными Института цитологии РАН и Института
органического синтеза имени И. Я. Постовского синтезировали соединения,
которые могут остановить дегенерацию нейронов при таких тяжёлых
заболеваниях, как болезнь Альцгеймера, болезнь Паркинсона и
черепно-мозговых травмах, — новые молекулы рядов индолил- и
пирролилазинов. Результаты исследования были опубликованы в 2021 году.</li></ul>
<p>Большие учёные вырастают из ребят, увлечённых познанием. Таковы
российские школьники, которые регулярно побеждают на международных
олимпиадах по разным предметам и делают первые шаги в науке. Ко Дню российской науки ЯКласс подготовили тест о русских
учёных, который познакомит вас с великими деятелями науки и
раскроет их с новой стороны.</p><p><span style="font-size: medium;"><a href="https://www.yaklass.ru/p/peremenka/yaklassnyj-test/test-ko-dniu-rossiiskoi-nauki-6809769" target="_blank"><b>Начать проходить тест</b></a></span><br /></p><p>Источник <a href="https://www.yaklass.ru/t-novosti/akcii-i-novosti-za-2022-god/stati-i-novosti-za-02-2022/neozhidannye-fakty-i-test-ko-dnyu-rossijskoj-nauki?mindbox-click-id=ff716b1e-9141-4496-9195-70d99d5f9317&utm_source=mindbox&utm_medium=email&utm_campaign=2022-02-04-t-test">https://www.yaklass.ru/t-novosti/akcii-i-novosti-za-2022-god/stati-i-novosti-za-02-2022/neozhidannye-fakty-i-test-ko-dnyu-rossijskoj-nauki?mindbox-click-id=ff716b1e-9141-4496-9195-70d99d5f9317&utm_source=mindbox&utm_medium=email&utm_campaign=2022-02-04-t-test</a><br /></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-79534606862132059382021-12-03T13:57:00.006+06:002021-12-03T13:57:55.237+06:00Вступительный балл серьезно повышен<div style="left: -99999px; position: absolute;">Приказ Министерства
науки и высшего образования Российской Федерации от 05.08.2021 №713 «Об
установлении минимального количества баллов единого государственного
экзамена по общеобразовательным предметам, соответствующим специальности
или направлению подготовки, по которым проводится прием на обучение в
образовательных организациях, находящихся в ведении Министерства науки и
высшего образования Российской Федерации, на 2022/23 учебный год». <p>Читать далее: <a href="https://4ege.ru/novosti-ege/62439-minimalnye-bally-ege-v-vuzy-minobrnauki-na-2022-2023-uchebnyj-god.html">https://4ege.ru/novosti-ege/62439-minimalnye-bally-ege-v-vuzy-minobrnauki-na-2022-2023-uchebnyj-god.html</a> </p></div><div style="left: -99999px; position: absolute;">Приказ Министерства
науки и высшего образования Российской Федерации от 05.08.2021 №713 «Об
установлении минимального количества баллов единого государственного
экзамена по общеобразовательным предметам, соответствующим специальности
или направлению подготовки, по которым проводится прием на обучение в
образовательных организациях, находящихся в ведении Министерства науки и
высшего образования Российской Федерации, на 2022/23 учебный год». <p>Читать далее: <a href="https://4ege.ru/novosti-ege/62439-minimalnye-bally-ege-v-vuzy-minobrnauki-na-2022-2023-uchebnyj-god.html">https://4ege.ru/novosti-ege/62439-minimalnye-bally-ege-v-vuzy-minobrnauki-na-2022-2023-uchebnyj-god.html</a> </p></div><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiruek64-h71rQ540EdZnIzsK6kfpdZ17lhn_Mp-S4RV8QQ_1whTRLNRL0fFT5l4JtbXzi5zlzATLgM_vgTQDBslMFTA9YNKlop4gSAlqX368bqrutrW96uRR3gnpvxyeTmPz2rbMvjMTM/s92/658249065.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="91" data-original-width="92" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiruek64-h71rQ540EdZnIzsK6kfpdZ17lhn_Mp-S4RV8QQ_1whTRLNRL0fFT5l4JtbXzi5zlzATLgM_vgTQDBslMFTA9YNKlop4gSAlqX368bqrutrW96uRR3gnpvxyeTmPz2rbMvjMTM/w200-h198/658249065.gif" width="200" /></a></div><!--[if gte mso 9]><xml>
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Министерства науки и высшего образования Российской Федерации от 05.08.2021
№713 «Об установлении минимального количества баллов единого государственного экзамена
по общеобразовательным предметам, соответствующим специальности или направлению
подготовки, по которым проводится прием на обучение в образовательных
организациях, находящихся в ведении Министерства науки и высшего образования
Российской Федерации, на 2022/23 учебный год». <br /></span><p></p><p>По всем предметам количество баллов увеличили.
Например, в 2021 году достаточно было набрать 36 баллов по русскому
языку и 27 – по математике.</p><p>В 2023 году понадобится получить уже
40 баллов по русскому языку и 39 баллов по математике. По остальным
предметам для поступления потребуется набрать минимум:</p><ul><li>обществознание – 45 баллов;</li><li>информатика и ИКТ – 44 балла;</li><li>литература и география – 40 баллов;</li><li>физика, биология и химия – 39 баллов;</li><li>история – 35 баллов;</li><li>иностранный язык – 30 баллов.</li></ul><div>Если
абитуриент предоставит баллы ЕГЭ ниже этих, вуз не вправе принимать
документы на поступление. В то же время каждый университет имеет право
установить собственные минимальные баллы, которые будут выше
утвержденных Минобрнауки.</div>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-47129627021600305922021-11-22T13:03:00.001+06:002021-11-24T22:20:18.126+06:00Концентрация кислоты<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSFiwoZ9fABOFmupf8zzWXJrvUc53cO5xdJvywuevctdjkVR6z2KKHsQrmxHocFgKwCzmvPXaKeWShF-QXu-w5Jx7zwCN_BHbkSq2LsoljfVHRG8ZlmchNyFcXduHQl8rAFx6Mjv7Tbo/s567/image002.gif" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="360" data-original-width="567" height="203" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvSFiwoZ9fABOFmupf8zzWXJrvUc53cO5xdJvywuevctdjkVR6z2KKHsQrmxHocFgKwCzmvPXaKeWShF-QXu-w5Jx7zwCN_BHbkSq2LsoljfVHRG8ZlmchNyFcXduHQl8rAFx6Mjv7Tbo/s320/image002.gif" width="320" /></a></div><br /> <b>Задача. </b>Имеется два сосуда. Первый содержит 5 кг, а второй - 15 кг раствора кислоты различной концентрации. Если эти растворы смешать, то получится раствор, содержащий 21% кислоты. Если же смешать равные массы этих растворов, то получится раствор, содержащий 22% кислоты. Сколько килограммов кислоты содержится в первом сосуде?<p></p><p><b>Решение. </b>Обозначим концентрацию в первом растворе через x, а во втором через y. Если смешать эти растворы получится раствор с концентрацией 5x + 15y =20 * 0.21, где<span></span></p><a name='more'></a><p></p><p>5 - кг, масса в первом сосуде</p><p>x - концентрация кислоты в первом растворе</p><p>15 - кг, масса во втором сосуде</p><p>y - концентрация кислоты во втором растворе</p><p>20 - кг, полученная при смешивании растворов </p><p>0,21 - содержание кислоты в растворе</p><p> А если смешать растворы с одинаковой массой m , то получится раствор с концентрацией mx + my = 2m * 0.22. Вместо m можно использовать числовые значения килограмм не больше 5, т. к. в первом сосуде всего 5 кг. При решении уравнения числовые значения перед x и y сократятся, а во второй части уравнения останется 2 * (концентрация кислоты в растворе). Получаем уравнение:</p><p>mx + my = (m+ m) * 0.22, где</p><p>m - масса в растворе</p><p>x и y - соответственно концентрация в первом и во втором сосудах</p><p>m + m - кг, масса, полученная при смешивании растворов </p><p>0.22 - концентрация кислоты в растворе</p><p>Получаем систему уравнений:</p><p>5x + 15y = 20 * 0.21</p><p>mx + my = 2m * 0.22</p><p>Рассмотрим второе уравнение:</p><p>mx + my = (m + m) * 0.22,</p><p>mx + my = 2m * 0.22, разделим его на m, получаем,</p><p>x + y = 2 * 0.22</p><p>x + y = 0.44</p><p>Выразим x, x = 0.44 - y</p><p>Теперь рассмотрим первое уравнение:</p><p>5x + 15y = 20 * 0.21, разделим обе части на 5</p><p>x + 3y = 4 * 0.21</p><p>x + 3y = 0.84</p><p>Подставим выражение, полученное из второго уравнения,</p><p>0.44 - y + 3y = 0.84.</p><p>2y = 0.4, разделим на 2 </p><p>y = 0.2</p><p>Теперь мы можем найти x, </p><p>x = 0.44 - 0.2</p><p>x = 0.24</p><p>Теперь, когда мы нашли x, мы можем найти количество кислоты в первом растворе,</p><p>5 * 0.24 = 1.2 (кг) количество кислоты в первом растворе.</p><p>Ответ: 1.2 кг количество кислоты в растворе.</p>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-24962623463546731552021-10-15T11:57:00.003+06:002021-11-24T22:28:14.381+06:00Нестандартное квадратное уравнение<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyTFIrD6OiTIwj42leNIhN6Gp_wavDvnGsZhFQB4zQJ4bkTKHxD7CmKEFKCHBnLz4MVcNaSeGrP1VTSlmgBBKNWuuOtdjq0zkhkBv2-iVx4i32DwCY-BQu0nz9ZM3qvn2YgQpOrz3kDRE/s278/logo.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="278" data-original-width="243" height="222" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyTFIrD6OiTIwj42leNIhN6Gp_wavDvnGsZhFQB4zQJ4bkTKHxD7CmKEFKCHBnLz4MVcNaSeGrP1VTSlmgBBKNWuuOtdjq0zkhkBv2-iVx4i32DwCY-BQu0nz9ZM3qvn2YgQpOrz3kDRE/w194-h222/logo.png" width="194" /></a></div><br /> Приведем два способа решения одной олимпиадной задачи 2021 года (школьный уровень).<p></p><p><b>Задача.</b> Найдите все решения уравнения <br /></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPqA6FfOCkk1DB-VBB62bNwB-ldfPkB3jgrPkiFA7z5NrkuBcqxKUAKGn2kj-_bXJYcw9mZEG4lSZ_Y-mcRRPF6ZIKL7aXmrpKTQ5IqZe-yQg3igHfWPqvt972klzGTlo68CVfs6ac3sdx/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="51" data-original-width="806" height="38" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPqA6FfOCkk1DB-VBB62bNwB-ldfPkB3jgrPkiFA7z5NrkuBcqxKUAKGn2kj-_bXJYcw9mZEG4lSZ_Y-mcRRPF6ZIKL7aXmrpKTQ5IqZe-yQg3igHfWPqvt972klzGTlo68CVfs6ac3sdx/w608-h38/image.png" width="608" /></a></div><br /><p></p><p><b>Первое решение. </b>Рассмотрим данное уравнение как квадратное относительно x. <span></span></p><a name='more'></a><br /><p></p><p>Найдем дискриминант </p><p>Д = (2siny)^2 - 4*1 </p><p>Д = 4(sin^2y -1 )</p><p>Так как дискриминант должен быть неотрицательным получаем</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfjWrsg13jC07JuoezDlJZvwqhvqK2CF7Eg9P99r4KguRvxgG5gXv1t25gGWppM-fTcdaiElJbjrIWt1vFuN1bGxCSbXCo2cOJw0dX_-zlXSGvR_S8u0JCHBGFcmcLARXsQd4yMCAPf0xO/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="68" data-original-width="357" height="61" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfjWrsg13jC07JuoezDlJZvwqhvqK2CF7Eg9P99r4KguRvxgG5gXv1t25gGWppM-fTcdaiElJbjrIWt1vFuN1bGxCSbXCo2cOJw0dX_-zlXSGvR_S8u0JCHBGFcmcLARXsQd4yMCAPf0xO/" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-HMlItHGuUQSzHvr3Z7FJVpfXS-gMa121AnaNGS79MH4G-Huv6uC1r0fNOT7SETHS7MgYbLrGKV0F-_XcrvSl2BoYnKNpWkXhWUVUYKhTmmGjcEK1VeYL181aMTd-kI3ksb6POsEtMhb2/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="69" data-original-width="317" height="70" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-HMlItHGuUQSzHvr3Z7FJVpfXS-gMa121AnaNGS79MH4G-Huv6uC1r0fNOT7SETHS7MgYbLrGKV0F-_XcrvSl2BoYnKNpWkXhWUVUYKhTmmGjcEK1VeYL181aMTd-kI3ksb6POsEtMhb2/" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO9yB5758ZZdSn4d9QbylOn2JV2f8JdNgqok8jx9AjU_khBEYuDxYEVajI-k06Tg_i5V_bBwAcgj_xJ-sqp_3t4Q5gzSDaDKDPgW3R0NYHBeNX4Z0Y-2gAR7FvY-vk8ERnBm54VaF_QmB0/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="69" data-original-width="284" height="78" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiO9yB5758ZZdSn4d9QbylOn2JV2f8JdNgqok8jx9AjU_khBEYuDxYEVajI-k06Tg_i5V_bBwAcgj_xJ-sqp_3t4Q5gzSDaDKDPgW3R0NYHBeNX4Z0Y-2gAR7FvY-vk8ERnBm54VaF_QmB0/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXWhafBQj8TbmKrOWK8nkUhV1kbNA4K_A2ZyvRL2_iHug0DyvRvXCZBbhyphenhyphenR__4WQ4cDU90f7WsThe_58vfbf32Y6cN_3HIVCVNhvDn9pDKj1NHsS_FvdK33-dWOolCEOgMpaKEYkhHfZ9F/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="76" data-original-width="457" height="66" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXWhafBQj8TbmKrOWK8nkUhV1kbNA4K_A2ZyvRL2_iHug0DyvRvXCZBbhyphenhyphenR__4WQ4cDU90f7WsThe_58vfbf32Y6cN_3HIVCVNhvDn9pDKj1NHsS_FvdK33-dWOolCEOgMpaKEYkhHfZ9F/w400-h66/image.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">Найдем x:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">1) при siny = 1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x^2 + 2x + 1 = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x = 1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">2) при siny = -1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x^2 - 2x -1 = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x = -1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><b>Второе решение:</b></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x^2 + 2xsiny + 1 = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Расписываем 1 по основному тригонометрическому тождеству</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x^2 + 2xsiny + sin^2y + cos^2y = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">(x + sin)^2 + cos^2y = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">cos^2y = 0</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIqwFTLHNuWueZW6orDahlI3CdKPu6vf2ZHvezJMa2VoXIhr0hpo7GnbsUigk4I93YqRgBhcdEwgD146iLvGGX2PigaepAX6ovq_CnNqJYb1tPmR3_x3zGzqlCl1lKNgU-rF8zja6mtHQH/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="76" data-original-width="457" height="53" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIqwFTLHNuWueZW6orDahlI3CdKPu6vf2ZHvezJMa2VoXIhr0hpo7GnbsUigk4I93YqRgBhcdEwgD146iLvGGX2PigaepAX6ovq_CnNqJYb1tPmR3_x3zGzqlCl1lKNgU-rF8zja6mtHQH/" width="320" /></a></div><br />В точках где cosy = 0, siny = 1, siny = -1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x= 1</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x = -1 </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br /></div><br /><p></p><p></p>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-7791628087985516782021-10-14T11:20:00.002+06:002021-10-14T11:22:13.085+06:00Неравенства между которыми одно целое число<p> Замените все символы "*" целыми числами так, чтобы только одно целое число удовлетворяло одновременно обоим неравенствам: x^2 + *x + * > 0 и x^2 + *x + * < 0</p><p>Рассмотрим уравнения (x -1 )(x - 3) > 0 и (x -2)(x - 5) < 0</p><p>При решения первого уравнения получаем: x < 1, x > 3</p><p>При решении второго уравнения получаем: 2 < x < 5</p><p>Между данными уравнениями только одно целое число - 4, значит данное неравенство удовлетворяет требованию задачи</p><p>Приведем еще несколько примеров таких неравенств:</p><p>(x - 2)(x - 5) > 0, x < 2 x > 5 </p><p>(x - 3 )(x - 7) < 0, 3 < x < 7</p><p>Здесь тоже только одно целое число - 6</p><p>(x - 3)(x - 7) > 0, x < 3 x > 7</p><p>(x - 4)(x - 9) < 0, 4 < x < 9</p><p>Целое число - 8 </p><p>(x - 4)(x - 7) > 0, x < 4 x> 7</p><p>(x - 5)(x - 11) < 0, 5 < x < 9</p><p>Целое число - 10 </p><p>(x - 5)(x - 11) > 0, x<5 x> 11</p><p>(x - 6)(x - 13) < 0 , 6 < x < 13</p><p>Целое число - 12</p><p>(x - 6)(x - 13) > 0, x < 6 x > 13</p><p>(x - 7 )(x - 15) < 0, 7 < x < 15</p><p>Целое число - 14</p><p>И так далее до бесконечности </p>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-14366464562941587452021-10-11T14:41:00.000+06:002021-10-11T14:41:01.714+06:00Катет в прямоугольном треугольнике<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgY1RJzAul01jLaZSO7HstlDNTZix-GViKSBgifDu_dJyLScfYuhz9aFhqJRQ4uT8YVYIiMob4kVdBMqB_vba_B5_EsahnSQBGGm7lJyyEJsKnYtFmx0jw_M5lLemoMyePa862EN9U_sTJG/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="378" data-original-width="677" height="179" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgY1RJzAul01jLaZSO7HstlDNTZix-GViKSBgifDu_dJyLScfYuhz9aFhqJRQ4uT8YVYIiMob4kVdBMqB_vba_B5_EsahnSQBGGm7lJyyEJsKnYtFmx0jw_M5lLemoMyePa862EN9U_sTJG/" width="320" /></a></div><br />По данным, изображенным на рисунке справа, найти длину катета BC прямоугольного треугольника ABC. <p></p><p><br /></p><p><br /></p><p><br /></p><p style="text-align: right;"><br /></p><p style="text-align: right;">Дано: треугольник ABC - прямоугольный</p><p style="text-align: right;">угол CAB = 60 градусов</p><p style="text-align: right;">угол ACB = 90 градусов</p><p style="text-align: right;">AM = MB </p><p style="text-align: right;">NM = 4</p><p style="text-align: right;">Найти катет BC - ?</p><p style="text-align: left;"><span></span></p><a name='more'></a>Первый способ решения:<p></p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic8ZlNB4u_15V40RKoR51Kkwg89rzWO4sMieBY7L9d_Yui84CrqfiPdBCg-xHFV5hLDs7p4rbyAXyb8zXFdwoP9waCAE64kBYbP8fT2JqCT6-a445fOMk1P9cHzKYaZ9HNkH5XgEnieprj/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="374" data-original-width="666" height="180" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEic8ZlNB4u_15V40RKoR51Kkwg89rzWO4sMieBY7L9d_Yui84CrqfiPdBCg-xHFV5hLDs7p4rbyAXyb8zXFdwoP9waCAE64kBYbP8fT2JqCT6-a445fOMk1P9cHzKYaZ9HNkH5XgEnieprj/" width="320" /></a></div><br />Рассмотрим треугольник ABC<p></p><p style="text-align: left;">угол ABC = 30 градусов, ABC = 180 - (CAB + ACB)</p><p style="text-align: left;">ABC = 180 - (90 + 60)</p><p style="text-align: left;">ABC = 180 - 150 </p><p style="text-align: left;">ABC = 30.</p><p style="text-align: left;">AC = 0,5AB, свойство угла в 30 градусов</p><p style="text-align: left;">Рассмотрим треугольник MNB</p><p style="text-align: left;">BN = 2MN, свойство угла в 30 градусов</p><p style="text-align: left;">BN = 8</p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikoTkkQW2XKtcTLucPtmSEO6X351Q6aKeJuNyBavrbDCKT5LAZNEjfeaOVIviJ5lMC-BVX3R7sYgaq0d45L0kGqGeZrkhwWSR10f2BULfCTfLmR3UkuRbickpLWvcd7w0inVFDGfG6sXcM/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="329" data-original-width="617" height="171" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikoTkkQW2XKtcTLucPtmSEO6X351Q6aKeJuNyBavrbDCKT5LAZNEjfeaOVIviJ5lMC-BVX3R7sYgaq0d45L0kGqGeZrkhwWSR10f2BULfCTfLmR3UkuRbickpLWvcd7w0inVFDGfG6sXcM/" width="320" /></a></div><br />Проведем медиану CM<p></p><p style="text-align: left;">CM = 0,5AB, свойство медианы проведенной к гипотенузе в прямоугольном треугольнике</p><p style="text-align: left;">Рассмотрим треугольник AMC</p><p style="text-align: left;">AM = CM,</p><p style="text-align: left;">Треугольник AMC - равнобедренный </p><p style="text-align: left;">угол ACM = 60 градусов, углы при основании равны</p><p style="text-align: left;">угол AMC = 60 градусов, 180 - 120</p><p style="text-align: left;">Рассмотрим треугольник CMB</p><p style="text-align: left;">CM = BM, </p><p style="text-align: left;">Треугольник CMB - равнобедренный </p><p style="text-align: left;">угол MCB = 30 градусов, углы при основании равны</p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiruUOn5mDGMvTbQp4hQ3u4_-l73EmMaNBwiVYGDMVQBSQHTkwqN9mm-K8TjCwgfIdWfTdhxx_vQzw6k5IoafZlRGJ8W1CEA0SM3lbHXFtO5jBY3tJ6E7RdwREW0h5nXgrksnkF7zlhBOVZ/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="345" data-original-width="652" height="169" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiruUOn5mDGMvTbQp4hQ3u4_-l73EmMaNBwiVYGDMVQBSQHTkwqN9mm-K8TjCwgfIdWfTdhxx_vQzw6k5IoafZlRGJ8W1CEA0SM3lbHXFtO5jBY3tJ6E7RdwREW0h5nXgrksnkF7zlhBOVZ/" width="320" /></a></div>угол CMB = 180 - (30 + 30)<p></p><p style="text-align: left;">CMB = 120 градусов</p><p style="text-align: left;">угол CMN = 120 - 90 </p><p style="text-align: left;">CMN = 30 градусов</p><p style="text-align: left;">Треугольник CMN - равнобедренный, так как углы при основании равны</p><p style="text-align: left;"><br /></p><p style="text-align: left;"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrnJ_dCVfTOU-J9b2iNE9o15u_aY3QKV2YKoz6x3y3b5Ks2BOXuckcFFniwFe5p1z6T_ij3uAc2RFjcOanHBTqsdRyUurlK3yyjCahKmMDity8tRBD8noeFwUxko2ywISj45a99CuuP9xz/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="347" data-original-width="623" height="178" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrnJ_dCVfTOU-J9b2iNE9o15u_aY3QKV2YKoz6x3y3b5Ks2BOXuckcFFniwFe5p1z6T_ij3uAc2RFjcOanHBTqsdRyUurlK3yyjCahKmMDity8tRBD8noeFwUxko2ywISj45a99CuuP9xz/" width="320" /></a></div><br /><br /><p></p><p style="text-align: left;"><br /></p><p style="text-align: left;"><br /></p><p><br /></p><p><br /></p><p>MCN = NMC = 30 градусов</p><p>MN = CN = 4</p><p>CB = CN + NB = 4 + 8</p><p>CB = 12 </p><p>Ответ: CB = 12</p><p>Второй способ решения:</p><p>угол ABC = 180 - (CAB + ACB)</p><p>ABC = 180 - (60 + 90)</p><p>ABC = 30</p><p>Рассмотрим треугольник MNB </p><p>BN = 2MN</p><p>BN = 8</p><p>Отрезок MN является серединным перпендикуляром к отрезку AB </p><p>Соединим точки A и N </p><p>AN = NB = 8, свойство серединного перпендикуляра</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs5sWICbaNysQ9eldtG2_IdDo0oVCzT3TlALW7zOcNPPITXLM9AFJrJyLQ7NWBvvL90pgaK6lYWVPPNirtMlSzAQVAaW0hx3kRLrHj00NH4lohu88iNd1ZhuARIROlw9wbq7F6Qk1ZkquZ/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="352" data-original-width="590" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhs5sWICbaNysQ9eldtG2_IdDo0oVCzT3TlALW7zOcNPPITXLM9AFJrJyLQ7NWBvvL90pgaK6lYWVPPNirtMlSzAQVAaW0hx3kRLrHj00NH4lohu88iNd1ZhuARIROlw9wbq7F6Qk1ZkquZ/" width="320" /></a></div>Треугольник ANB - равнобедренный, т.к <p></p><p>AN = NB</p><p>угол NAB = 30 градусов, углы при основании равны</p><p>Рассмотрим треугольник ACN</p><p>угол CAN = 30 градусов</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilprLsXUE8SCemCSnOvNEYHmXNp7DPWq6Aw4ho-poMNvTwnGiCBjCiZYmWrrKH3Fzzy03UkmXrXa2-8lWu6zhue0K019thW-H6ybR8OBcGW1TUm4vPYb_19NCjdB9GYCWIOreXjaFtjtSO/" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="" data-original-height="321" data-original-width="567" height="181" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilprLsXUE8SCemCSnOvNEYHmXNp7DPWq6Aw4ho-poMNvTwnGiCBjCiZYmWrrKH3Fzzy03UkmXrXa2-8lWu6zhue0K019thW-H6ybR8OBcGW1TUm4vPYb_19NCjdB9GYCWIOreXjaFtjtSO/" width="320" /></a></div><br /><br />CN = 4, катет лежащий против угла в 30 градусов<p></p><p>CB = CN + NB </p><p>CB = 4 + 8</p><p>CB = 12 </p><p><br /></p><p>Ответ: CB = 12 </p>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com1tag:blogger.com,1999:blog-7075323357155470607.post-73838921741895615072021-10-07T13:10:00.002+06:002021-10-07T13:10:46.166+06:00Единицы на доске<p><span style="font-family: "Times New Roman", serif;"></span></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjf9vGZrx7juUHsZwJtOd6XvBCMqPTTr7uOZayuOkwQ-kQ28aLzgj6zY04XNVqqJCZTth3u8sJv6ZZ_WCEhfR05b9nOoRMH4mWnjJYeonfkaLv4IcKOFQHP7QdkwVS-wiw5KKls62Fh90wtv9MJytyK-_AYKszGYq52s7uoq7FU__EswAJsZd_AF1aePw=s337" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="150" data-original-width="337" height="142" src="https://blogger.googleusercontent.com/img/a/AVvXsEjf9vGZrx7juUHsZwJtOd6XvBCMqPTTr7uOZayuOkwQ-kQ28aLzgj6zY04XNVqqJCZTth3u8sJv6ZZ_WCEhfR05b9nOoRMH4mWnjJYeonfkaLv4IcKOFQHP7QdkwVS-wiw5KKls62Fh90wtv9MJytyK-_AYKszGYq52s7uoq7FU__EswAJsZd_AF1aePw=s320" width="320" /></a></div><br />На доске
написано <i><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><i><span lang="EN-US" style="font-family: "Times New Roman","serif";">
</span></i><span style="font-family: "Times New Roman", serif;">единиц, между некоторыми
из которых поставили знаки + и посчитали сумму. Например, если изначально было
написано </span><i><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><span style="font-family: "Times New Roman", serif;"> = 12 единиц, то могла
получиться, например, такая сумма:</span><p></p>
<p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Times New Roman","serif";">1 + 11 + 11 + 111 + 11 + 1 + 1 =
147.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">а) Могла
ли сумма равняться 150, если </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif";">
</span></i><span style="font-family: "Times New Roman","serif";">= 60?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">б) Могла
ли сумма равняться 150, если </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><span style="font-family: "Times New Roman","serif";"> = 80?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">в) Чему
могло равняться </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><span style="font-family: "Times New Roman","serif";">, если полученная сумма
чисел<span style="mso-spacerun: yes;"> </span>равна 150?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Решение:<span></span></span></p><a name='more'></a>
<o:p></o:p><p></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">а) Да.
Можно взять число 111, тогда остается еще 57 единиц, даже если взять 57 раз по
1, то сумма будет равна 168. Значит нужно брать число 11, остальные по 1 и
постепенно увеличивать количество чисел 11 в записи, получаем такие суммы: <o:p></o:p></span></p>
<p class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">11
+ 58 = 69<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">11
+ 11 + 56 = 78<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">11
+ 11 + 11 + 54 = 87<o:p></o:p></span></p>
<p class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -18.0pt;"><!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">11+
11 + 11+ 11 + 52 = 96<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Можно
заметить, что при увеличении количества числа 11 в записи, количество единиц в
записи уменьшается на 2, то есть вся сумма числа увеличивается на 9, 11 – 2 =
9.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Получаем
суммы равные: 69, 78, 87, 96, 105, 114, 123, 132, 141, 150<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Для
получения суммы равной 150 нужно, взять число 11 10 раз, и остальные 40 чисел
по 1.<o:p></o:p></span></p><p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Приведем другой пример решения:</span></p><p class="MsoNormal"><span style="font-family: Times New Roman, serif;">Возьмем число 111, остается 57 единиц, если взять 57 раз по 1, сумма будет 168. значит возьмем число 11 и несколько единиц, получим такую сумму:</span></p><p class="MsoNormal"><span style="font-family: Times New Roman, serif;">11 + 1 + 1 + 1 + 1 = 15; сумма единиц равна 15, количество единиц 6. Чтобы получить сумму равную 150, нужно взять 150/15 = 10 таких пар, количество единиц при этом будет равно 10*6 = 60. Чтобы получить сумму равную 150, нужно взять 10 пар с суммой 11 + 1 + 1 + 1 + 1 = 15.</span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">б) Нет.
Также как и в случае с </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif";">
</span></i><span style="font-family: "Times New Roman","serif";">= 60, если взять
число 111 сумма чисел будет больше 150. Значит будем брать по 11, остальные по
1 и постепенно увеличивать количество чисел 11 в записи. Как и в случае с </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif";"> = </span></i><span style="font-family: "Times New Roman","serif";">60, сумма будет увеличиваться на
9. Но так как количество единиц в записи больше, суммы будут другие и будут
равны: 89, 98, 107, 116, 125, 134, 143, 152. <o:p></o:p></span></p>
<p align="center" class="MsoNormal" style="text-align: center;"><span style="font-family: "Times New Roman","serif";">143<150<152.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">в) Вернемся
к </span><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif"; mso-ansi-language: EN-US;">n</span></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "Times New Roman","serif";">
</span></i><span style="font-family: "Times New Roman","serif";">= 60 и вспомним,
что при увеличении количества числа 11 в записи суммы, сумма увеличивается на
9. Запишем любое число при записи которого используются числа 11 и 1 и их сумма
равна 150:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">11 + 11
+ 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 1 + 1 + 1 + 1 + 1 + 1
+ 1 + 1 = 150.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">В записи
этого числа используется 33 единицы, если мы уменьшим количество чисел 11 в
записи, то получим:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">11 + 11
+ 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11+ 1 + 1 + 1 + 1 + 1 + 1 + 1 +
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 150.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">В записи
этого числа мы получаем 42 единицы<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">При
увеличении количества чисел 11 в записи, мы уменьшаем количество чисел 1 в
записи суммы на 9 и наоборот, если уменьшать количество чисел 11 в записи
суммы, то количество 1 увеличивается на 9. Так как мы можем взять количество
чисел 11 от 0 до 13. Мы получаем следующее количество единиц в записи суммы:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">150,
141, 132, 123, 114, 105, 96, 87, 78, 69, 60, 51, 42, 33. <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Но при
записи мы также можем использовать число 111, но только один раз, значит будем
использовать числа 11 и 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">При
использовании числа 111 получаем следующие суммы:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">111 + 11
+ 11 + 11 + 11 + 1 + 1 + 1 + 1 + 1 + 1 = 150 (6 раз по 1)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">111 + 11
+ 11 + 11 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 +1 + 1 + 1 + 1 + 1 + 1 + 1 =
150 (17 раз по 1)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">111+ 11
+ 11 +<span style="mso-spacerun: yes;"> </span>1 + 1 + 1 ……. + 1 = 150 (28 раз
по 1)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">111 + 1
+ 1 + 1 ……+ 1 = 150 (39 раз по 1)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">Количество
единиц в этих суммах: 15, 24, 33. 42.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">При
совмещении мы получаем прогрессию: <o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-family: "Times New Roman","serif";">150,
141, 132, 123, 114, 105, 96, 87, 78, 69, 60, 51, 42, 33, 24, 15.<o:p></o:p></span></p>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-61715103846504258222021-10-06T11:33:00.000+06:002021-10-06T11:33:03.394+06:00Как увеличить свою долю<p> </p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgiUiP3eblGb-JCWg9hstl7ariV71qvDwi3mJ39uV6wOuG4E-ey9IH4th1BcUNNtK8qczZIT0pZIlTgXYUeZsaHVLWw0PoKZbUWrD8zxYCS171J3Z2nPT7VqiT04iTsDe-0ADWGP6I7SswGZYoMKRO40mBHuq1U98z0O0U3R72yS2gdXigBWzCE31M01w=s286" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="286" data-original-width="176" height="286" src="https://blogger.googleusercontent.com/img/a/AVvXsEgiUiP3eblGb-JCWg9hstl7ariV71qvDwi3mJ39uV6wOuG4E-ey9IH4th1BcUNNtK8qczZIT0pZIlTgXYUeZsaHVLWw0PoKZbUWrD8zxYCS171J3Z2nPT7VqiT04iTsDe-0ADWGP6I7SswGZYoMKRO40mBHuq1U98z0O0U3R72yS2gdXigBWzCE31M01w" width="176" /></a></div><br />Борис и Иван вложили деньги в общий бизнес. После этого один
из них добавил еще <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">1 млн рублей</i></b>, в результате чего его доля в бизнесе увеличилась <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">на 0,05</i></b>,
а когда он добавил <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">еще 1 миллион рубле</i></b>й, его доля увеличилась <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">еще на 0,04</i></b>. Сколько миллионов
рублей ему нужно добавить, чтобы увеличить <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">свою долю еще на 0,06</i></b>?<o:p></o:p><p></p><p class="MsoNormal"><br /></p><p class="MsoNormal">Решение:<span></span></p><a name='more'></a><p></p><p class="MsoNormal">x - общая сумма денег вложенных в бизнес</p><p class="MsoNormal">y - сумма вложенная одним бизнесменом</p><p class="MsoNormal">y/x - доля одного из бизнесменов</p><p class="MsoNormal">t - сумма денег вложенных в бизнес (в миллионах рублей)</p><p class="MsoNormal">Получаем уравнение: </p><p class="MsoNormal"></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpvNzY9uECGM3sO1_P5NJEb7fy4z6C7PYdhe4gBoVYVgHpSLOYxhxb6OKYoqI8BOXnTVuuyDktih30fg-_1N5yf20uqtwjJU-zprfM0Upz-gUCDzddhtGUdb1UbyzCgZ3is9dA6x3Mlxw2/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="66" data-original-width="393" height="54" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhpvNzY9uECGM3sO1_P5NJEb7fy4z6C7PYdhe4gBoVYVgHpSLOYxhxb6OKYoqI8BOXnTVuuyDktih30fg-_1N5yf20uqtwjJU-zprfM0Upz-gUCDzddhtGUdb1UbyzCgZ3is9dA6x3Mlxw2/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div>Тогда,<div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHBDqRch1pR4IYNl3wLG6pLyUt9mNrPn-DuCwStGbrc0FAf06oAq5SQH9cthZmUda1fF-s7Yw2smzr1Lw4bxXsSc4Beep8PiADKSjUQnroKMR-kmqDpY95Bo5l-ag3E5bYlzTGt3An1mBk/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="103" data-original-width="393" height="84" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHBDqRch1pR4IYNl3wLG6pLyUt9mNrPn-DuCwStGbrc0FAf06oAq5SQH9cthZmUda1fF-s7Yw2smzr1Lw4bxXsSc4Beep8PiADKSjUQnroKMR-kmqDpY95Bo5l-ag3E5bYlzTGt3An1mBk/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Решаем систему уравнений:</div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj03tbjrLn8azvIEzJXAVDaec-N1o8EMgi4A-YTtWg3C0j58x7CMCzaMN6Ls3BqfT6fSjS4N38uaavXkSVhoTDMazDE0RL6LaPaKJEt5jKfmNHWWFd9otHtpDLqkZiN7OeF2fiJITuDCLZ/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="111" data-original-width="446" height="80" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjj03tbjrLn8azvIEzJXAVDaec-N1o8EMgi4A-YTtWg3C0j58x7CMCzaMN6Ls3BqfT6fSjS4N38uaavXkSVhoTDMazDE0RL6LaPaKJEt5jKfmNHWWFd9otHtpDLqkZiN7OeF2fiJITuDCLZ/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuXdJUCXifGbqWKU77JlJVeeAy2eNDL7mwEsdzDSCCGEBxp5g5FgXlpkF3xFqwaURQ2Act4w-6zvhvTSKCaJYEDrBD4TJyvJjom59h-XWBAHhz-YSbyI_ke-Tn4jXIz3lKddF2eWrJXitV/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="110" data-original-width="324" height="109" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjuXdJUCXifGbqWKU77JlJVeeAy2eNDL7mwEsdzDSCCGEBxp5g5FgXlpkF3xFqwaURQ2Act4w-6zvhvTSKCaJYEDrBD4TJyvJjom59h-XWBAHhz-YSbyI_ke-Tn4jXIz3lKddF2eWrJXitV/" width="320" /></a></div><div class="separator" style="clear: both; text-align: left;">Приравниваем левые части уравнений и получаем:</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">0,05(x + 1) = 0,09 (0,5x + 1) | * 100</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">5x + 5 = 4,5x + 9 | * 2</div><div class="separator" style="clear: both; text-align: left;">\</div><div class="separator" style="clear: both; text-align: left;">10x + 10 = 9x + 18</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">x = 8</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Найдем y, </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtsaY9V6PUX6nojng1Luu9iOj5o1xs956VMMOqPdDO5Lw-b0oGL38zAVdaK7PuOyitpai7yzx9opduKLH8eqUZPRYiaYa-ZQaJcZnyclo9_dwFL4vuAv2ol6oeipdRi94tbtBZtOE31cbR/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="99" data-original-width="399" height="79" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtsaY9V6PUX6nojng1Luu9iOj5o1xs956VMMOqPdDO5Lw-b0oGL38zAVdaK7PuOyitpai7yzx9opduKLH8eqUZPRYiaYa-ZQaJcZnyclo9_dwFL4vuAv2ol6oeipdRi94tbtBZtOE31cbR/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj46qmglR0LURK2a-Bf14BlWBww_cRVAuDqIjatrBrs3Wq1jhMaBkK-ZFF6wcX0axKqlKMB65w8YoRIwuJq85M49eITr2gIho_cN08YQjbQYTdARwNLekeyMYbdQvePQMHg1lSq023lh0BY/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="76" data-original-width="377" height="65" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj46qmglR0LURK2a-Bf14BlWBww_cRVAuDqIjatrBrs3Wq1jhMaBkK-ZFF6wcX0axKqlKMB65w8YoRIwuJq85M49eITr2gIho_cN08YQjbQYTdARwNLekeyMYbdQvePQMHg1lSq023lh0BY/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">y = 4,4 </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Изначально доля бизнесмена составляла 4.4/8 = 0,55, после внесения дополнительного миллиона 4.4 + 1/8+1 = 0,6, после внесения второго миллиона 5,4 + 1/ 9+1 = 0,64. Для решения задачи, нужно чтобы доля бизнесмена увеличилась еще на 0,06, то есть стала равна 0,64 + 0,06 = 0,7. Обозначим нужное число миллионов через <b><i>a</i></b> и получим следующее уравнение: </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJjh09z_s7zAI6gh54iqaTNWeWYqzR4uyZgLYjwe-0_9ImnvTeqTDMWWlQ3qO0abOqypRcqiAqcNcVHRY32xbfJSJ4zoBvFat8tdVxVWVQiLjLiFbJU4NGvgRG6LPzpgXf6CJ8NQMRGHN9/" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="101" data-original-width="358" height="90" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiJjh09z_s7zAI6gh54iqaTNWeWYqzR4uyZgLYjwe-0_9ImnvTeqTDMWWlQ3qO0abOqypRcqiAqcNcVHRY32xbfJSJ4zoBvFat8tdVxVWVQiLjLiFbJU4NGvgRG6LPzpgXf6CJ8NQMRGHN9/" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">6,4 + a = 7 + 0,7a </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">0,3a = 06</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">a = 2</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Ответ: Нужно добавить 2 миллиона </div><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br /></div><br /><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;"><br /></div><br /><br /></div><br /><br /></div><br /><br /></div><br /><br /><div><p></p><p class="MsoNormal"><br /><br /></p></div></div>Максим Кривошеинhttp://www.blogger.com/profile/04682370417073300221noreply@blogger.com1tag:blogger.com,1999:blog-7075323357155470607.post-18358571816216477782021-01-03T09:05:00.002+06:002021-01-03T09:05:32.614+06:00Навигатор самостоятельной подготовки к ГИА<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgVdh3Ityl_SlnNOexzA_UY30VTjib8lVN1xFC8tnrJBM9hL5i39JJGE52d6PbdqGmapyx1__KQ7F1G9eGXrCRMRb862Uj9AD9mE8Zvz5X0h9aYVh5UnQtD7craq2w9NE3l_HDduUKeos/s600/032.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="566" data-original-width="600" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgVdh3Ityl_SlnNOexzA_UY30VTjib8lVN1xFC8tnrJBM9hL5i39JJGE52d6PbdqGmapyx1__KQ7F1G9eGXrCRMRb862Uj9AD9mE8Zvz5X0h9aYVh5UnQtD7craq2w9NE3l_HDduUKeos/s320/032.jpg" width="320" /></a></div> Федеральный институт педагогических
измерений (ФИПИ) открыл на своем официальном сайте <br />новый раздел
«Навигатор подготовки», в котором публикуются материалы для
самостоятельной подготовки обучающихся к государственной итоговой
аттестации.
<p></p><p style="text-align: justify;">Раздел включает: </p><p style="text-align: justify;"><a href="https://fipi.ru/navigator-podgotovki/navigator-oge"><b>«Навигатор самостоятельной подготовки к ОГЭ»</b> </a><br /><a href="https://fipi.ru/navigator-podgotovki/navigator-ege#ma"><b>«Навигатор самостоятельной подготовки к ЕГЭ»</b>.</a> </p><p style="text-align: justify;">В данном разделе уже опубликованы рекомендации по самостоятельной
подготовке к ЕГЭ и ОГЭ по всем предметам. Не реже одного раза в месяц в
нем будут публиковаться и другие материалы, включающие описание
проверяемого содержания и умений, ссылки на соответствующие главы и
параграфы учебников федерального перечня Минпросвещения России, уроки
Российской электронной школы, задания открытых банков ОГЭ и ЕГЭ.
Публикации будут выходить до апреля 2021 года включительно.</p>
<p style="text-align: justify;">Навигатор подготовки можно посмотреть на <a href="https://fipi.ru/navigator-podgotovki" rel="external" target="_blank" title="title"> сайте.</a></p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-80226265580419301562021-01-03T07:27:00.004+06:002021-01-03T07:27:42.483+06:00Изменен порядок проведения ЕГЭ и ГИА<p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAv_p8JR8-O0e1cSPufw0fv7plWfhE0qeZ1nIL-_bWvHiMG9Cu3qMzfWYqfQ8C5BspgphGnuQUszfnH8z3zXWkDWh1gd-RKzy_Cehj9t_ulk5Zjq0SqikJ8tG31GHW08ZwSEnOXkK0bTg/s1841/%25D1%2581%25D0%25BE%25D0%25B2%25D0%25BE%25D0%25BA%25D1%2583%25D0%25BF+001.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1841" data-original-width="1385" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjAv_p8JR8-O0e1cSPufw0fv7plWfhE0qeZ1nIL-_bWvHiMG9Cu3qMzfWYqfQ8C5BspgphGnuQUszfnH8z3zXWkDWh1gd-RKzy_Cehj9t_ulk5Zjq0SqikJ8tG31GHW08ZwSEnOXkK0bTg/s320/%25D1%2581%25D0%25BE%25D0%25B2%25D0%25BE%25D0%25BA%25D1%2583%25D0%25BF+001.jpg" /></a></div> <b>Объявлены изменения порядка проведения ЕГЭ и государственной итоговой аттестации <br />выпускников 9-х и 11-х классов в 2021 году.</b><p></p><p>Минпросвещения и Рособрнадзор объявили о решениях, которые приняты в
отношении порядка проведения ЕГЭ и государственной итоговой аттестации
выпускников 9-х и 11-х классов в 2021 году.</p><p class="speech">«Мы понимаем, что для ребят, которые сдают ЕГЭ в 2021
году, это год непростой. В связи с принятыми мерами на фоне
эпидемиологической ситуации мы внесли изменения в правила сдачи
экзаменов. Проведение итогового сочинения или изложения в этом учебном
году запланировано на вторую декаду апреля. Государственная итоговая
аттестация по образовательным программам среднего общего образования в
формате ЕГЭ должна пройти с 31 мая по 2 июля, дополнительный период ЕГЭ –
с 12 по 17 июля», – сказал Сергей Кравцов.</p>
<p>Для выпускников 11-х классов и других участников ЕГЭ досрочный период
проведения экзаменов в связи с текущей эпидемиологической обстановкой в
2021 году отменяется.</p>
<p>Для получения аттестата о среднем общем образовании выпускникам,
которые не планируют поступать в вузы, вместо ЕГЭ нужно будет сдать
государственный выпускной экзамен (ГВЭ) по двум предметам – русскому
языку и математике.<span></span></p><a name='more'></a><p></p>
<p>Выпускникам, которые собираются поступать в вузы и будут сдавать для
этого ЕГЭ, чтобы получить аттестат, достаточно сдать на
удовлетворительный результат ЕГЭ по русскому языку. ЕГЭ по математике
базового уровня в 2021 году проводиться не будет.</p>
<p>ГВЭ для выпускников 11 классов пройдёт в конце мая, а основной период
ЕГЭ следом – ориентировочно с 31 мая по 2 июля 2021 года для всех
участников экзаменов, в том числе для выпускников прошлых лет.</p>
<p>Для участников ЕГЭ, которые не смогут сдать экзамены в основные сроки
по болезни или иной уважительной причине, будет предусмотрен
дополнительный период проведения ЕГЭ в середине июля 2021 года. Эти
сроки будут увязаны с графиком приемной кампании в вузы – все, кто будет
сдавать ЕГЭ в дополнительный период, так же, как и участники основного
периода, успеют получить свои результаты и подать документы в выбранные
учебные заведения.</p>
<p>Итоговое сочинение и изложение, которые являются для 11-классников
допуском к государственной итоговой аттестации, пройдут в середине
апреля.</p>
<p>Для 9-классников досрочный период проведения государственной итоговой аттестации также отменён.</p>
<p>Аттестаты за 9-й класс об основном общем образовании будут выданы на
основании результатов государственной итоговой аттестации только по двум
обязательным предметам<span> – </span>русскому языку и математике. В 2021 году выпускники 9-х классов не будут сдавать на ОГЭ учебные предметы по выбору.</p>
<p>Для девятиклассников также будут проведены контрольные работы по
одному учебному предмету по их выбору. Результаты этих контрольных не
будут влиять на получение аттестата и допуск к итоговой аттестации.
Контрольные работы пройдут с 17 по 25 мая 2021 года. Конкретные даты
определят региональные органы управления образованием либо школы.</p>
<p>Государственная итоговая аттестация (ГИА-9) по русскому языку и
математике будет проведена в период с 24 по 28 мая 2021 года, резервные
сроки проведения основного периода ГИА-9 придутся на начало июня 2021
года. Для девятиклассников, не сдавших экзамены в основной период, ГИА-9
по русскому языку и математике пройдёт повторно в дополнительный
сентябрьский период.</p>
<p class="speech">«Данные решения приняты в интересах здоровья и
безопасности всех участников и организаторов экзаменов, чтобы снизить
эпидемиологические риски и сделать проведение итоговой аттестации
школьников в 2021 году максимально безопасным. При проведении экзаменов
также будут применены все рекомендованные Роспотребнадзором меры
эпидемиологической безопасности, которые успешно зарекомендовали себя на
ЕГЭ в 2020 году и позволили предупредить новый всплеск заболеваемости
после экзаменов»,<span> – </span>прокомментировал изменения руководитель Рособрнадзора Анзор Музаев.</p><p class="speech">Источник <a href="https://edu.gov.ru/press/3285/obyavleny-izmeneniya-poryadka-provedeniya-ege-i-gosudarstvennoy-itogovoy-attestacii-vypusknikov-9-i-11-klassov-v-2021-godu/">https://edu.gov.ru/press/3285/obyavleny-izmeneniya-poryadka-provedeniya-ege-i-gosudarstvennoy-itogovoy-attestacii-vypusknikov-9-i-11-klassov-v-2021-godu/</a> <br /></p><p> </p>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-23275149074354430252020-11-05T20:35:00.002+06:002020-11-05T20:35:34.344+06:00Бесплатная подготовка к экзаменам<h1 class="block__header" data-v-30d03f76="" data-v-c7ab5a18="" data-v-e63fa3d0="" style="margin-bottom: 16px;">
<span style="font-size: small;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq_-EYf3bmXpqmbpY29NubMX6P3vpBtX5eNqvsg-GSTmBVSNX81bE8l55HNDLbfp7K7GAczRLyFMRIjbldlXj_XsEEGXjyvW5XZLhTiBmnDQnVlkQ429ZFWo1dV56xRE1mRVmb-swzB_U/s573/%25D0%259C%25D0%2590%25D0%259A%25D0%25A1%25D0%2598%25D0%259C%25D0%25A3%25D0%259C.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="525" data-original-width="573" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhq_-EYf3bmXpqmbpY29NubMX6P3vpBtX5eNqvsg-GSTmBVSNX81bE8l55HNDLbfp7K7GAczRLyFMRIjbldlXj_XsEEGXjyvW5XZLhTiBmnDQnVlkQ429ZFWo1dV56xRE1mRVmb-swzB_U/s320/%25D0%259C%25D0%2590%25D0%259A%25D0%25A1%25D0%2598%25D0%259C%25D0%25A3%25D0%259C.png" width="320" /></a></div>Бесплатная подготовка к ОГЭ и ЕГЭ от MAXIMUM. Онлайн уроки 2 раза в неделю.<br /><br /></span></h1> <ul class="list header-list point" data-v-30d03f76="" data-v-e63fa3d0="" data-v-f4550db0=""><li data-v-f4550db0="">Занимайся в онлайн-группах по математике и русскому языку</li><li data-v-f4550db0="">Тренируйся каждый день в приложении</li><li data-v-f4550db0="">Решай варианты на тренажёре Решутест</li></ul><p><span style="font-size: medium;"><b><a href="https://online.maximumtest.ru/?utm_source=email%20marketing%20Mailigen&utm_campaign=%2020201003_teacher_reshutest&utm_medium=email" target="_blank"> Жми сюда</a></b></span><br /></p><h2 data-v-a18b50ac="" data-v-e63fa3d0="">Расписание занятий</h2> <h4 data-v-a18b50ac="" data-v-e63fa3d0=""><span style="font-size: small;">ЕГЭ Математика Вторник 16:00-17:15 Пятница 16:00-17:15</span></h4><div class="flex-container row column" data-v-a18b50ac="" data-v-e63fa3d0="" style="align-items: center; justify-content: space-between;"> <div class="ui-card card" data-v-261e05a8="" data-v-a18b50ac="" data-v-e63fa3d0=""><h5 data-v-261e05a8="" data-v-a18b50ac=""><span style="font-size: small;">Русский язык Воскресенье 11:30-12:45 Четверг 17:30-18:45</span></h5></div></div><span style="font-size: small;"> </span><h4 data-v-a18b50ac="" data-v-e63fa3d0=""><span style="font-size: small;">ОГЭ Математика Вторник 17:30-18:45 Четверг 17:30-18:45</span></h4><div class="flex-container row column" data-v-a18b50ac="" data-v-e63fa3d0="" style="align-items: center; justify-content: space-between;"> <div class="ui-card card" data-v-261e05a8="" data-v-a18b50ac="" data-v-e63fa3d0=""><h5 data-v-261e05a8="" data-v-a18b50ac=""><span style="font-size: small;">Русский язык Воскресенье 10:00-11:15 Среда 17:30-18:45</span></h5></div></div>Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0tag:blogger.com,1999:blog-7075323357155470607.post-15658256963518823382020-06-08T13:54:00.001+06:002020-06-08T13:54:33.545+06:00Квадрат в треугольнике<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSn7moLrBTjfuoY-GqDhx50kPy0roK4lxk7Nv90jmt8VavmN1Ro5aPDMbmGgi2VaVhx7Q0YRwbK8wukYEFhmK6gQv3QjeNDwz5YOu0WdQMg2Rxl976qAKDbwUlqMBa9OwQlHKUoJ9MsNE/s1600/%25D0%25A2%25D1%2580%25D0%25B5%25D1%2583%25D0%25B3+%25D0%25B8+%25D0%25BA%25D0%25B2%25D0%25B0%25D0%25B4%25D1%2580%25D0%25B0%25D1%2582.png" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="213" data-original-width="354" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSn7moLrBTjfuoY-GqDhx50kPy0roK4lxk7Nv90jmt8VavmN1Ro5aPDMbmGgi2VaVhx7Q0YRwbK8wukYEFhmK6gQv3QjeNDwz5YOu0WdQMg2Rxl976qAKDbwUlqMBa9OwQlHKUoJ9MsNE/s320/%25D0%25A2%25D1%2580%25D0%25B5%25D1%2583%25D0%25B3+%25D0%25B8+%25D0%25BA%25D0%25B2%25D0%25B0%25D0%25B4%25D1%2580%25D0%25B0%25D1%2582.png" width="320" /></a><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Продолжим подготовку к ЕГЭ 2020 по математике. Рассмотрим
решение задачи 16 в 46 варианте сборника контрольных измерительных материалов <b style="mso-bidi-font-weight: normal;">«ЕГЭ-2020. Математика. Профильный уровень. 50
вариантов. Типовые варианты экзаменационных заданий от разработчиков ЕГЭ». Под
редакцией И.В. Ященко.</b></span></div>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span style="font-weight: normal; mso-bidi-font-weight: bold;"> </span></h4>
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Задача 1.<span style="font-weight: normal; mso-bidi-font-weight: bold;"> Вершины К и L квадрата KLMN с центром О
лежат на стороне АВ треугольника АВС, а вершины М и N-на сторонах ВС и АС
соответственно. Высота СН треугольника АВС проходит через точку О и пересекает
отрезок MN в точке D, причём CD=DO=ОН.</span></h4>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span style="font-weight: normal; mso-bidi-font-weight: bold;">а) Докажите, что треугольник АВС равнобедренный и
прямоугольный.</span></h4>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span style="font-weight: normal; mso-bidi-font-weight: bold;">б) Пусть прямая AD пересекает сторону ВС в точке Q.
Найдите AQ, если сторона квадрата KL =1. <a name='more'></a></span></h4>
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<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Решение. </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">а)<b style="mso-bidi-font-weight: normal;"> </b>Рассмотрим треугольники </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDC</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDO</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.
Они прямоугольные, так как СН перпендикулярна АВ, а значит и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">MN</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> (прямые АВ и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">MN</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
параллельны, как прямые, содержащие противоположные стороны квадрата). Треугольники
</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDC</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDO</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> имеют общий
катет </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">ND</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и равные по условию катеты </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">DC</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">DO</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">. Значит треугольники </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDC</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">NDO</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равны. Аналогично, равны треугольники М</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">DC</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> и М</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">DO</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">. Поскольку </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">О и МО равны как половинки диагоналей квадрата, то </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">СМО – ромб. Но угол </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">ОМ
прямой (диагонали квадрата перпендикулярны), то </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">СМО
– квадрат. Следовательно </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">С=СМ и угол АСВ –
прямой. Далее заметим, что треугольники АВС и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">СМ
подобны по первому признаку, так как имеют общий угол С и соответственные углы
АВС и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">МС при параллельных АВ и </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">М
и секущей ВС равны. Следовательно, треугольник АВС, как и треугольник </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">N</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">СМ прямоугольный и равнобедренный.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">б)
Предлагаю тригонометрическое решение этой задачи. Из прямоугольного треугольника
А</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Н тангенс угла </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">АН
равен отношению </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">D</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Н : АН = 1 : 1,5
= 2/3. Но угол </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CAQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> равен разности
углов ВАС и В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">.Так как угол ВАС<span style="mso-spacerun: yes;">
</span>равен 45 градусам, а его тангенс равен 1, то по формуле тангенса
разности аргументов получаем <span style="mso-spacerun: yes;"> </span></span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CAQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">
= </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">(ВАС – В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">) = (</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">ВАС – </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">)/(1+ </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> ВАС * </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">tg</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">В</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">AQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">) = (1 – 2/3)/(1
+ 1*2/3) = 1/5. Значит </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">cos</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CAQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> = 5</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">/</span><span lang="EN-US" style="font-family: Symbol; font-size: 12.0pt; mso-ansi-language: EN-US; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">√</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">26. </span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Так
как АН = СН = 1,5, то по теореме Пифагора АС = 1,5</span><span style="font-family: Symbol; font-size: 12.0pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Symbol;"><span style="mso-char-type: symbol; mso-symbol-font-family: Symbol;">√</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2. Из треугольника </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CAQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> имеем по определению синуса </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> = АС/</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">cos</span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> </span><span lang="EN-US" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; mso-ansi-language: EN-US;">CAQ</span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;"> = 1,5</span>√<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2*</span>√<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">26/5 = 3</span>√<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">13/5.</span></div>
<div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Ответ 3</span></b><b>√</b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">13/5.</span></b></div>
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<br /></div>
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<br /></div>
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<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Нашел в сети несколько решений следующей
задачи, но у всех разные ответы. Попробуйте найти правильный ответ.</span></i></div>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
Задача 2. <span style="font-weight: normal; mso-bidi-font-weight: bold;">Вершины К и L квадрата KLMN с центром О лежат
на стороне АВ треугольника АВС, а вершины М и N-на сторонах ВС и АС
соответственно. Высота СН треугольника АВС проходит через точку О и пересекает
отрезок MN в точке D, причём CD=DO=ОН.</span></h4>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span style="font-weight: normal; mso-bidi-font-weight: bold;">а) Докажите, что треугольник АВС равнобедренный и
прямоугольный.</span></h4>
<h4 style="margin-bottom: .0001pt; margin: 0cm;">
<span style="font-weight: normal; mso-bidi-font-weight: bold;">б) Пусть прямая AD пересекает сторону ВС в точке Q.
Найдите AQ, если сторона квадрата KL =2. </span></h4>
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Олег Кривошеинhttp://www.blogger.com/profile/11804950706356583803noreply@blogger.com0