证明：∵OB, OC分别平分∠ABC,∠ACB, ∴∠MBO＝∠OBC, ∠NCO＝∠OCB 　　又∵MN∥BC,且MN经过点O,∴∠MOB＝∠OBC, ∠NOC＝∠OCB,∴MO＝MB, NO＝NC 　　∴△AMN的周长=AM＋MN＋AN＝AM＋MO＋NO＋AN＝AM＋MB＋NC＋AN＝AB＋AC