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Консультация № 196687
16.10.2019, 17:15
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Здравствуйте! Прошу помощи в следующем вопросе:
Равнобедренная трапеция описана около окружности, а ее периметр равен 15. Найдите проекцию диагонали трапеции на ее большее основание.
Равнобедренная трапеция описана около окружности, а ее периметр равен 15. Найдите проекцию диагонали трапеции на ее большее основание.
Обсуждение
20.10.2019, 19:46
общий
Извините за беспокойство! Предлагаю продлить срок действия консультации на пять суток.
Об авторе:
Facta loquuntur.
Facta loquuntur.
21.10.2019, 15:42
общий
это ответ
Здравствуйте, sasha.yakimova9976@gmail.com!
Рисунок к задаче находится в прикреплённом файле.
Отрезки касательных к окружности, проведённые из одной точки, равны и составляют равные углы с прямой, проходящей через эту точку и центр окружности [1, с. 167]. Можно доказать, что в равнобедренной трапеции ABCD, прямая EG, проходящая через середины оснований трапеции, -- её ось симметрии. Следовательно,
Литература
1. Геометрия. 7 -- 9 классы : учебник для общеобразовательных учреждений / Л. С. Атанасян и др. -- М.: Просвещение, 2010. -- 384 с.
Рисунок к задаче находится в прикреплённом файле.
Отрезки касательных к окружности, проведённые из одной точки, равны и составляют равные углы с прямой, проходящей через эту точку и центр окружности [1, с. 167]. Можно доказать, что в равнобедренной трапеции ABCD, прямая EG, проходящая через середины оснований трапеции, -- её ось симметрии. Следовательно,
|AG|=|BG|=|AF|=|BH|=a,
|DE|=|CE|=|DF|=|CH|=b,
|AB|=|AG}+|BG|=a+a=2a -- длина большего основания трапеции,
|CD|=|CE|+|DE|=b+b=2b
-- длина меньшего основания трапеции,|AD|=|AF|+|DF|=a+b=|BH|+|CH|=|BC| -- длина боковой стороны трапеции,
P=|AB|+|BC|+|CD|+|AD|=2a+(a+b)+2b+(a+b)=4a+4b=4(a+b) -- периметр трапеции,
|AC'|=|AG|+|GC'|=|AG|+|CE|=a+b=4(a+b)/4=P/4=15/4=3,75 (ед. длины) -- искомая длина проекции.
Литература
1. Геометрия. 7 -- 9 классы : учебник для общеобразовательных учреждений / Л. С. Атанасян и др. -- М.: Просвещение, 2010. -- 384 с.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
21.10.2019, 15:44
общий
Адресаты:
Прошу извинить за прикрепление не того файла, который нужен! Рисунок к рассмотренной задаче прикреплён ниже.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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