Certificate: ∠ ABC+∠ ACB = 180-∠ A

∠a 1 = 180- 1/2(∠ABC+∠ACB)

∠A 1 = 180- 1/2( 180-∠A)

∠A 1=90+ 1/2∠A

(2)

It is proved that the bisector as ∠ACB passing through point C passes through point BA 1

∠bqc = 90+ 1/2∠a from( 1)

Because ∠QCA 1=90

So ∠A 1=∠BQC-90.

So ∠ a1=1/2 ∠ a.