Question

如图,点A.B.C在⊙O上,AB⊥BC于点D,AE平分∠BAC交⊙O于点E,求证AE平分OAD\

Answer 1

连结OE,

AE平分∠BAC,

∴∠BAE＝∠CAE,

∴弧BE＝弧CE,

∴OE⊥BC,

又∵AD⊥BC,

∴OE∥AD,

∴∠AEO＝∠DAE,

又∵AO＝OE,

∴∠OAE＝∠AEO,

∴∠OAE＝∠DAE,

∴AE平分∠OAD