△ABC中,∠A=60°,BE平分∠ABC,CF平分∠ACB,BE,CF相交于点O,试问OE与OF有何关系,

Question

△ABC中,∠A=60°,BE平分∠ABC,CF平分∠ACB,BE,CF相交于点O,试问OE与OF有何关系,

Answer 1

∵BE平分∠ABC,CF平分∠ACB ∴∠ABE=∠ACF,∠EBC=∠FCB ∵∠A=60° ∴180°- ∠A=∠ABC+∠ACB 即:∠ACB+∠ABC=120° ∴2分之1(∠ACB+∠ABC)=∠EBC+∠FCB=60° ∴180°- (∠EBC+∠FCB)=180°- 60°=120° ∴OE和OF之...