解：OD平分∠BOE∴∠EOD＝1/2∠BOE∵OF平分∠AOE∴∠EOF＝1/2∠AOE∴∠FOD＝∠EOD+∠EOF＝1/2∠BOE+1/2∠AOE＝1/2（∠BOE+∠AOE）∵∠BOE+∠AOE＝∠AOB＝180∴∠FOD＝90∴OF⊥OD
