BC切圆O于B,AB＝BC＝OA,连AC交圆O于D,OC交圆O于E则∠CED的度数为（ ）

BC切圆O于B,AB＝BC＝OA,连AC交圆O于D,OC交圆O于E则∠CED的度数为（ ）
BC切圆O于B,AB＝BC＝OA,连AC交圆O于D,OC交圆O于E则∠CED的度数为（ ）

BC切圆O于B,AB＝BC＝OA,连AC交圆O于D,OC交圆O于E则∠CED的度数为（ ）
97.5°
∠OBC=90°,OA=AB=OB,∠OBA=60°
AB=BC===>∠BAC=∠BCA=(180-90-60)/2=15°
∠BOD=2∠BAC=30°
∠DOC=15====>∠DAE=7.5°
∠DEA=15+30=45°
∠CEA=180-7.5-30=142.5°
∠CED=142.5-45=97.5°

连接OD
OA=OB=AB
∠OAB=∠OBC=∠AOB=60
OB=BC
∠BOC=∠BCO=45
AB=AC,∠OBC=90
∠ABC=150
∠BAC=(180-150)/2=15
∠CED
=180-∠OED
=180-(180-∠DOE)/2
=90+∠DOE/2
=90+(∠AOC-∠AOD...

全部展开

连接OD
OA=OB=AB
∠OAB=∠OBC=∠AOB=60
OB=BC
∠BOC=∠BCO=45
AB=AC,∠OBC=90
∠ABC=150
∠BAC=(180-150)/2=15
∠CED
=180-∠OED
=180-(180-∠DOE)/2
=90+∠DOE/2
=90+(∠AOC-∠AOD)/2
=90+(135-(180-2∠0AC))/2
=90+(2∠OAC-45)/2
=90+(2(60-∠BAC))/2
=90+(60-15)
=135

收起