已知圆O的弦AB垂直于直径CD,垂足为F,点E在AB上,且EA=EC,延长EC到点P,连接PB,使PB=PE.是否AC2=AE*AB

已知,EA = EC ,可得：∠ACE = ∠CAE .
CD是AB的垂直平分线,可得：AC = BC ,则有：∠BAC = ∠ABC .
在△ACE和△ABC中,∠ACE = ∠CAE = ∠BAC = ∠ABC ,
所以,△ACE ∽ △ABC ,
可得：AC/AB = AE/AC ；
即有：AC^2 = AE×AB .