1令AB是直径,O是圆心,C是圆周上异于A、B的任意一点则：OA=-OB,|OA|=|OB|=|OC|=RAC=OC-OABC=OC-OB故：AC·BC=(OC-OA)·(OC-OB)=|OC|^2+OA·OB-OC·(OA+OB)=R^2-R*Rcos(π)-OC·0=R^2-R^2=0故：AC⊥BC即：∠ACB=π/22...