如图,在△ABC中,∠ABC的角平分线与∠ACB的外角平分线交于点D,求证∠A=2∠D

如图,在△ABC中,∠ABC的角平分线与∠ACB的外角平分线交于点D,求证∠A=2∠D
如图,在△ABC中,∠ABC的角平分线与∠ACB的外角平分线交于点D,求证∠A=2∠D

如图,在△ABC中,∠ABC的角平分线与∠ACB的外角平分线交于点D,求证∠A=2∠D
对于△ABC,有∠ACE=∠A+∠ABC=∠A+2∠DBC①
对于△DBC,有∠ACE=2∠DCE=2(∠D+∠DBC)=2∠D+2∠DBC②
①-②可得∠A-2∠D=0
∴∠A=2∠D