AB+AC>BP+PC。BP+PC=BD-PD+PC=BD+PC-PD
证明：延长BA到D，使AD=AC，连PD∵ PA是角平分线∴∠CAP=∠DAP∵AC=AD，AP=AP∴△ACP≌△ADP∴PC=PD∵PB+PD＞AB+AD∴PB+PC＞AB+AC
BP＋PC＜BP＋PD＋CD＝BD＋CD＜AB＋AD＋CD＝AB＋AC所以BP＋PC＜AB＋AC
