Question

平面几何证明题：

Answer 1

∵CF平分∠ACB,∴∠GCO=1/2∠ACB,

∵OG⊥BC,∴∠COG=90°-1/2∠ACB,

∵BE、AD平分∠ABC、∠BAC,

∴∠BOD=∠OAB+∠OBA

=1/2(∠ABC+∠BAC)

=1/2(180°-∠ACB)

=90°-1/2∠ACB,

∴∠BOD=∠COG.