Question

如图所示,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.

Answer 1

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 .