Question

如图①所示,在△ABC中,D是边BC延长线上一点,∠ABC的平分线BO与∠ACD的平分线CO交于点O,试探求∠A与∠BO

Answer 1

∵CO是∠ACD的平分线

∴∠DCO=∠ACD/2

又∠ACD=∠A+∠ABC,∠DCO=∠OBC+∠BOC

∴∠OBC+∠BOC=（∠A+∠ABC）/2

∠BOC=∠A/2+∠ABC/2-∠OBC

又BO是∠ABC的平分线,

∴∠OBC=∠ABC/2

∴∠BOC=∠A/2