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
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
答
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...