Question

如图,△ABC的三个顶点在⊙O上,AD⊥BC,D为垂足,E是BC⌒的中点

求证：∠EAO=∠EAD

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