如图在三角形abc中角b等于60度角平分线ad ce交于点o求证ac等于ae加cd

如图,在AC上取一点F,使得AE=AF,连接OF∵AD是三角形ABC的角平分线∴∠EAO=∠FAO∵AO=AO∴△AEO≌△AFO（SAS）∠AOE=∠AOF∵CE是三角形ABC的角平分线∴∠ACE=∠BCE在△AOC中∠AOC=180°-∠FAO-∠ACO=180°-1/2(∠ACB+∠BAC）=120°∵∠AOE+∠AOC=180°∴∠AOE=60°则∠COD=60°∠COF=60°∴∠COD=∠COF∵CO=CO∴△COD≌△COF(ASA)CD=CF∴AE+CD=AF+CF=AC