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.

问题描述:

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.
证明: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...