Question

Rt△ABC中,∠ABC=90°,以AB为直径的圆O交AC于点D,过点D的切线交BC于E, ①求证

Answer 1

1、证明：连接OD、OE∵∠ABC＝90∴BC切圆O于点B∵DE切圆O于点D∴BE＝DE∵OB＝OD,OE＝OE∴△OBE全等于△ODE∴∠BOE＝∠DOE∴∠BOD＝2∠DOE∵OA＝OD∴∠OAD＝∠ODA∴∠BOD＝∠OAD+∠ODA＝2∠ODA∴∠DOE＝∠ODA∴OE∥AC...