如图,在△ABC中,∠A=60°,DB、DC分别平分∠ABC、∠ACB,EB、EC分别平分∠DBC、∠DCB,求∠BDE

Question

如图,在△ABC中,∠A=60°,DB、DC分别平分∠ABC、∠ACB,EB、EC分别平分∠DBC、∠DCB,求∠BDE

Answer 1

连接AD,D为△ABC的内心,E为△DBC的内心
∠BDE=∠CDE=1/2∠BDC
∠BDC=180°-(∠DBC+∠DCB)
=180°-1/2(∠B+∠C)
=180°-1/2(180°-∠A)
=90°+1/2∠A
=120°
∠BDE=1/2×120°=60°