Question

三角形abc中,角bac,角abc的平分线交于点o,ao交bc于d,角aob与角cof有何数量关系

Answer 1

如图,已知三角形ABC中,角BAC、角ABC的平分线交于O,AO交BC于D,BO交AC于E,连OC,过O作OF垂直于BC于F,(1)试判断角AOB与角COF有何数量关系∵∠BAC、∠ABC的平分线交于O

∴OC平方∠ACB

那么∠BCO=∠FCO=1/2∠ACB

∵∠AOB=180°-(∠BAO+∠ABO)

=180°-1/2(∠BAC+∠ABC)

=180°-1/2[180°-∠ACB]

=90°+1/2∠ACB

OF⊥BC,那么RT△COF中：∠COF=90°-∠FCO=90°-1/2∠ACB

∴∠AOB+∠COF=90°+1/2∠ACB+90°-1/2∠ACB=180°