Предмет: Геометрия, автор: yanatimofeeva

В окружности с центром О,АС и ВД диаметры .Центральный угол АОД равен 112 градусов. Найдите вписанный угол АСВ

Ответы

Автор ответа: Вика0123456789

2 способа решения: 1) угол АОД и ВОС- вертикальные--> равны друг другу--> 112° ∆ВОС равнобедренный (т.к. ВО и ОС -радиусы окружности) Значит в нём угол С равен углу В = (180-112):2= 34° ( угол С-искомый угол АСВ) 2)угол АОД и АОВ-смежные--> АОВ=180-112=68° Но угол АОВ является центральным и опирается на дугу АВ. Угол АСВ-вписанный,и также опирается на дугу АВ--> равен половине центрального угла АОВ=68:2=34 :)

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