Question

如图.BD、CD是三角形ABC的平分线、求证角BOC∠BOC＝90°＋∠A

Answer 1

证明：延长BD交AC于E

∵BD平分∠ABC

∴∠ABD＝∠ABC/2

∴∠BEC＝∠A+∠ABD＝∠A+∠ABC/2

∵CD平分∠ACB

∴∠ACD＝∠ACB/2

∴∠BOC＝∠BEC+∠ACD

＝∠A+（∠ABC+∠ACB）/2

＝∠A+（180-∠A）/2

＝90+∠A/2