已知圆o的弦CD与直径AB垂直于F,点E在CD上,且AE=CE.求证,CA²=CE·CD

^2是平方直径AB⊥弦CD,由垂径定理得AB平分CD,所以AB垂直平分CD则AC=AD,得∠ACD=∠D又AE=CE,所以∠CAE=∠ACE,所以∠CAE=∠D由∠CAE=∠D,且公共角∠ACE=∠DCA得△CAE∽△CDA,所以CA/CD=CE/CA即CA^2=CE*CD