如图,在△ABC中,AB=AC,∠A=36°,线段AB的垂直平分线交AB于D,交AC于E,连接BE. 求证:(1)BE=BC; (2)AE2=AC•EC.

问题描述:

如图,在△ABC中,AB=AC,∠A=36°,线段AB的垂直平分线交AB于D,交AC于E,连接BE.
求证:(1)BE=BC;
(2)AE2=AC•EC.

证明:(1)∵AB=AC,∠A=36°,∴∠ABC=∠C=72°,∵DE是AB的中垂线,∴AE=BE,∴∠ABE=36°,∴∠EBC=36°,∴∠CEB=72°,∴∠CEB=∠C,∴BE=BC;(2)∵∠A=∠EBC=36°,∠C=∠C,∴△ABC∽△BEC,∴AB:BC=BC:...