It is known that in △ ABC, ad, be and CF are bisectors of three internal angles and intersect with point O, og ⊥ BC, and the perpendicular foot is g

It is known that in △ ABC, ad, be and CF are bisectors of three internal angles and intersect with point O, og ⊥ BC, and the perpendicular foot is g

prove:
∵∠ BOD = ∠ ABO + ∠ Bao = ∠ BAC / 2 + ∠ ABC / 2 = (180 degrees - ∠ ACB) / 2 = 90 degrees - ∠ ACB / 2
=90 degrees - OCB
∠ GOC = 90 degrees - ∠ OCB
∴∠BOD=∠GOC