因为CD=DB
A0=0B
所以AC//0D
∠0DB=∠ACB
∠ABC=∠0BD
∠CAB=180-∠ACB-∠扒颤纯洞穗ABC
∠DOB=180-∠0BD-∠0DB
∠A0D=180-∠DOB=∠0BD+∠春咐0DB
∠CAB+∠AOD=180-∠ACB-∠ABC+∠0BD+∠0DB=180
∠0DE=360-90-180=90
DE是⊙O的切线
证贺键明:
∵雀大BA=2BO,BC=2BD,∠ABC=∠OBD
∴△ABC∽△OBD
∴∠DOB=∠CAB
∴∠EAO+∠DOA=∠DOB+∠DOA=180°
∵四边形OAED内角和为360°,且∠AED=90°
∴∠ODE=360°-∠AED-(∠EAO+∠DOA)=90°
∴OD⊥DE
∵OD是圆O的半径
∴顷拍竖DE是⊙O的切线