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Вопрос по геометрии:
в окружности с центром в точке о и радиусом равным 8 см проведена касательная BC (B-точка касания) Найдите длину отрезка OC если BC=15-
Автор:
buddy73
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Дано:
Окружность с центром в точке О
Радиус(r) = 8
ВС - Касательная к окружности, в точке касания В
ВС = 15
Найти: ОС
Решение:
1)Радиус, проведенный к касательной в точке касания, перпендикулярна к касательной
=> ОВ перпендикулярен к ВС
2)Проведём ОС, увидим, что треугольник ВОС прямоугольный( так как угол ОВС 90° )
Из этого следует, что ОС в квадрате(^2) = ОВ^2 + ВС^2
теперь подставим числа:
ОС^2 = 8^2 + 15^2 = 64 + 225 = 289
ОС =
что равняется 17.
Ответ: 17
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