已知,AD是△ABC的角平分线,BE⊥AD.CF⊥AD,垂足分别为E,F,BF和EC的延长线交与点P,连接AP,求证:C

2个回答

  • 证明:延长BE和AC,交于点M.

    BE⊥AE,则∠AEB=∠AEM=90°;

    又∠BAE=∠MAE,AE=AE,则⊿BAE≌ΔMAE(ASA),EB=EM.

    ∵BE⊥AE;CF⊥AE,则BE∥FC.

    ∴AF/AE=FC/EM=FC/EB=PC/PE.

    即AF/AE=PC/PE,AF/FE=PC/CE,则CF∥AP.