Предмет: Геометрия, автор: Mintaka

Касательные в точках A и B к окружности с центром O пересекаются под углом 24°. Найдите угол ABO. Ответ дайте в градусах.

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Автор ответа: ulasovage

0

Обозначим точку пересечения касательных буквой С .
По свойству касательных, проведённых к окружности из одной точки :
АС=ВС.
Рассмотрим Δ АВС - равнобедренный ⇒ ∠ САВ=∠СВА =(180°-24°)/2=78°
ОА ⊥ АС Значит ∠ САО= 90°
Аналогично ∠ СВО= 90°.
∠АВО= ∠СВО - ∠СВА=90° - 78°= 12°
ОТВЕТ :12°

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