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Консультация № 146282
07.10.2008, 00:27
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Здравствуйте, помогите пожалуйста
Угол при основании равнобедренного треугольника равен α. Найти площадь описанного около треугольника круга, если радиус вписанной в треугольник окружности равен r.
Угол при основании равнобедренного треугольника равен α. Найти площадь описанного около треугольника круга, если радиус вписанной в треугольник окружности равен r.
Обсуждение
Неизвестный
07.10.2008, 04:17
общий
это ответ
Здравствуйте, Arkalis!
Треугольник АВС
Отрезок АО он же R делит угол а пополам (из определения вписанных окружностей)
R, r и половина основания образуют прямоугольный треугольник, из которого:
sin(a)=r/R => R=r/sin(a)
Площадь круга получается пR^2=п(r/sin(a))^2
Треугольник АВС
Отрезок АО он же R делит угол а пополам (из определения вписанных окружностей)
R, r и половина основания образуют прямоугольный треугольник, из которого:
sin(a)=r/R => R=r/sin(a)
Площадь круга получается пR^2=п(r/sin(a))^2
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