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Консультация № 146111
05.10.2008, 17:48
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Пожалуйста,помогите решить задачу.
В прямоугольную трапецию вписана окружность радиуса 1 см. Найти стороны трапеции, если её большее основание равно 4 см.
В прямоугольную трапецию вписана окружность радиуса 1 см. Найти стороны трапеции, если её большее основание равно 4 см.
Обсуждение
Неизвестный
05.10.2008, 20:15
общий
это ответ
Здравствуйте, Артемьев Дмитрий Михайлович!
Проводим перпендикуляр из центра на боковую сторону, и два основания.
Так как две касательные из одной точки к окружности равны получаем такой расклад:
Одно основание перпендикуляр поделил на части 1 и 3.
Второе - на части 1 и x
Боковая сторона тогда равна 3+x
Если провести высоту из второй вершины меньшего основания, будет прямоугольный треугольник с основанием 3-x, высотой 2, и гипотенузой 3+х
Составляем уравнение и решаем.
Проводим перпендикуляр из центра на боковую сторону, и два основания.
Так как две касательные из одной точки к окружности равны получаем такой расклад:
Одно основание перпендикуляр поделил на части 1 и 3.
Второе - на части 1 и x
Боковая сторона тогда равна 3+x
Если провести высоту из второй вершины меньшего основания, будет прямоугольный треугольник с основанием 3-x, высотой 2, и гипотенузой 3+х
Составляем уравнение и решаем.
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