Question

如图，△ABC的三个顶点在⊙O上，AD⊥BC，D为垂足，E是弧BC的中点。 求证：∠EAO＝∠EAD

急急急急

Answer 1

证明：

连接OB，则

∠AOB=2*∠ACB，∠OAB=∠OBA

∵AD⊥BC

∴∠OAB
=(1/2)(180°-∠AOB)
=90°-(1/2)∠AOB
=90°-∠ACB
=∠DAC

∵E是弧BC的中点

∴∠EAB=∠EAC

∴∠EAO
=∠EAB-∠OAB
=∠EAC-∠DAC
=∠EAD

得证

谢谢