Question

如图,已知OM、ON分别是∠AOB、∠BOC的平分线,射线OP在∠AOB的内部,若要使∠AOP=∠MON,则OP应满足什

Answer 1

因为OM平分∠AOB,ON平分∠BOC

∠MOB=∠AOB/2,∠NOB=∠BOC/2

所以,∠MON

=∠MOB+∠NOB

=∠AOB/2+∠BOC/2

=(∠AOB+∠BOC)/2

=∠AOC/2

要使∠AOP=∠MON=∠AOC/2

则OP应是∠AOC的平分线