AD=AE
∠DAP=∠EAP
AP=AP
ΔDAP≌ΔEAP
DP=EP
∠ADP=∠AEP
∠DPB=∠EPC
∴∠DBP=∠ECP
ΔBDP≌ΔCEP
BD=EC
AB=AC
AP平分∠BAC
所以AP垂直于BC