Предмет: Геометрия, автор: катюша407

Хорда АВ равна 38 см. ОА и ОВ радиусы окружности ,причем угол АОВ равен 90° Найдите расстояние от точки О до хорды АВ

Ответы

Автор ответа: murchik09

пусть OC - искомое расстояние. тогда:

треугольник АВО прямоугольный равнобедренный(ОА=ОВ=r), АС=СВ (так как в равнобедренном треугольнике высота является медианой(угол ОСА=углуОСВ=90 градусов из условия)), значит АС=СВ=9 (см)

так как треугольник АОВ прямоугольный, то медиана, проведенная к гипотенузе равна половине гипотенузы: ОС=АС=9 (см)

ОТВЕТ: 9см

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