Question

如图,已知△ABC中,AD平分∠BAC交BC于D,∠ABC、∠ACB的平分线交AD于O,过O作OE⊥BC于E.

Answer 1

1.∠BOD=∠ABO+∠BAO=(∠ABC+∠BAC)/2=(π -∠ACB)/2=(π -2∠OCB)/2

即∠BOD=π/2-∠OCB

2.因为∠EOC=π/2-∠OCB

所以∠BOD=∠EOC