Question

如图,OA,OB,OC都是圆O的半径,若角AOB=2角BOC,那么角ACB=2角BAC成立吗?为什么?

Answer 1

由于圆心角是同弧圆周角的两倍,

有∠AOB = 2∠ACB,∠BOC = 2∠BAC,

又∠AOB = 2∠BOC,

故∠ACB = 1/2 * ∠AOB = 1/2 * 2∠BOC = ∠BOC = 2∠BAC.