已知:如图所示,AD为△ABC的角平分线,P为AD上一点,若AB>AC.试说明:AB-AC>PB-PC

过C作CF垂直AD交AB于F,交AD于E,连接PF
∵∠FAE=∠CAE,∠AEF=∠AEC=90°AE=AE
∴△AFE≌△ACE,AF=AC,BF=AB-AF=AB-AC
∵AF=AC,AP=AP,∠FAP=∠CAP
∴△AFP≌△ACP,PF=PC,BF+PF＞BP,BF+PC＞BP
∵BF=AB-AC
∴AB-AC+PC＞BP,AB-AC＞BP-PC