证明:∵PB=PC∴∠PBC=∠PCB∵∠PBA=∠PCA∴∠PBC+∠PBA=∠PCB+∠PCA即∠ABC=∠ACB所以AB=AC又AP=AP,PB=PC∴△PAB≌△PAC∴∠PAB=∠PAC即AP平分∠BAC