连结OA
∵AB=AC,BO=CO,AO=AO
∴△ABO≌△AOC
延长AO交BC与D
∵AB=AC
∴∠ABC=∠ACB
∵∠ABO=∠ACO
∴∠OBC=∠OCB
∵OD=OD,BO=CO,∠OBC=∠OCB
∴△ODB≌△CDO
∴∠ADB=∠ADC=1/2*180°=90°
∴AO⊥BC