Question

如图,△ABC的两个外角的平分线BF、CF相较于点F,求证:∠F=90°-1/2∠A

Answer 1

∵∠FBC=1/2(∠A+∠ACB)

∠FCB=1/2(∠A+∠ABC)

∴∠F=180°-∠FBC-∠FCB

∴ ∠F=180°-∠A-1/2∠ACB-1/2∠ABC

∵1/2∠ACB+1/2∠ABC+1/2∠A=90°

所以整理可得∠F=90°—1/2∠A.