已知△ABC内接于⊙o,AO为半径,AD⊥BC于点D,求证:角BAD=角OAC(多种方法)
问题描述:
已知△ABC内接于⊙o,AO为半径,AD⊥BC于点D,求证:角BAD=角OAC(多种方法)
答
证明:延长AO交圆O于E,连接CE
∵AD⊥BC
∴∠ABC ∠BAD=90
∵∠AEC、∠ABC所对应圆弧都为弧AC
∴∠AEC=∠ABC
∵直径AE
∴∠OAC ∠AEC=90
∴∠OAC ∠ABC=90
∴∠OAC=∠BAD