如图,过△ABC的顶点B和C分别作AB、AC的垂线BD与CD两线交点D,过点C作CE⊥AD交AB于E,交AD于F,求证:AC2=AE•AB.
问题描述:
如图,过△ABC的顶点B和C分别作AB、AC的垂线BD与CD两线交点D,过点C作CE⊥AD交AB于E,交AD于F,求证:AC2=AE•AB.
答
证明:∵△AFC∽△ACD,
∴
=AC AD
,AF AC
∴AC2=AD•AF.
∵△AFE∽△ABD,
∴
=AF AB
,AE AD
∴AB•AE=AD•AF,
∴AC2=AB•AE.