Question

已知∠aob=2∠boc求证∠acb=2∠bac

如图2-1-8 已知⊙O中 ∠ AOB =2∠ BOC .求证:∠ ACB =2∠ BAC . 图2-1-8

Answer 1

思路解析:圆周角∠ ACB 与圆心角∠ AOB 对同一条弧 所以∠ ACB = ∠ AOB 同理 ∠ BAC = ∠ BOC 再利用已知条件可得结论. 证明:∠ ACB = ∠ AOB ∠ AOB =2∠ BOC ∠ ACB =∠ BOC ∠ BAC = ∠ BOC ∠ ACB =2∠ BAC .