Question

OA⊥OD,OD为∠BOC的平分线,OE为BO的延长线,∠COE的度数是否为∠AOB的度数的2倍?如果是,请说明理由.

Answer 1

如图所示,延伸AO至F,∠AOB+∠BOD=90,∠BOD=∠COD,所以∠AOD+∠COD=90, 又因为∠COD+∠COF=90,所以,∠AOB=∠COF,因为对顶角∠AOB=∠EOF,所以∠COE=∠COF+∠EOF=2∠AOB.