1、∵AD平分∠BAC∴∠BAD＝∠BAC/2∵BO平分∠ABC∴∠ABO＝∠ABC/2∴∠BOD＝∠BAD+∠ABO＝（∠BAC+∠ABC）/2＝（180°-∠ACB）/2＝90°-∠ACB/2∵CO平分∠ACB∴∠BCO＝∠ACB/2∵OE⊥BC∴∠COE+∠BCO＝90°∴∠COE＝90°-∠BCO＝90°-∠ACB/2∴∠BOD＝∠COE
2、AB平方=17平方=289AC平方+BC平方=8平方+15平方=289∴AB平方=AC平方+BC平方∴△ABC是直角三角形,AC、BC是直角边∵O是三角形内心∴O到三边的距离相等=OE∴S△ABC=S△AOB+S△AOC+S△BOC =1/2AB×OE+1/2AC×OE+1/2BC×OE =1/2OE(AB+AC+BC)∵S△ABC=1/2AC×BC∴OE=AC×BC/(ab+ac+bc) =8×15/(17+8+15) =3