Предмет: Геометрия, автор: ozodayusupova168

Даю 10 баллов быстро с чертежём AB и BC хорда окружности с центром O, угол ABC 30 градусов. Найти длину хорды AC если радиус окружности 10 см ответ с чертежём и отвечайте

ozodayusupova168: Ответьте please

Ответы

Автор ответа: vov44k

Ответ:

10 см

Объяснение:

1. Проведём радиусы OA, OC. OA = OC = 10 см

2. Вписанный ∠ABC опирается на дугу AC. Центральный ∠AOC опирается на дугу AC. Тогда ∠AOC = 2 · ∠ABC = 2 · 30° = 60°

3. Р/м ΔAOC:

OA = OC = 10 см

∠AOC = 60°

⇒ ∠OAC = ∠OCA = (180° - ∠AOC)/2 = 60° ⇒ ΔAOC -- равносторонний ⇒ AC = OA = OC = 10 см

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