|
连接OC,OD
∠COB=∠CAB+∠DBA=2∠CAB
∠DOA=2∠DBA
∠DOA+∠COB=180-∠COD
∠AEB=180-(∠DAB+∠CAB)=180-1/2*(∠DOA+∠COB)=180-1/2(180-∠COD)=180-90+∠COD/2=90+∠COD/2
∠COD/2=∠AEB-90=180-∠DEA-90=90-∠DEA
CD/AB=(CD/2)/R(在三角形DOC中,即为∠COD/2的正弦值)
sin(∠COD/2)=sin(90-∠DEA)=cos∠DEA
选D |
