一道数学几何题,急需啊啊``````````````````过三角形ABC的顶点C作一条直线与边AB及中线AD分别交于点E和F.过D做DM平行FC交AB于M,说明AE*FB*=2AF*ED

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一道数学几何题,急需啊啊``````````````````过三角形ABC的顶点C作一条直线与边AB及中线AD分别交于点E和F.过D做DM平行FC交AB于M,说明AE*FB*=2AF*ED
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一道数学几何题,急需啊啊``````````````````过三角形ABC的顶点C作一条直线与边AB及中线AD分别交于点E和F.过D做DM平行FC交AB于M,说明AE*FB*=2AF*ED
一道数学几何题,急需啊啊``````````````````
过三角形ABC的顶点C作一条直线与边AB及中线AD分别交于点E和F.过D做DM平行FC交AB于M,说明AE*FB*=2AF*ED

一道数学几何题,急需啊啊``````````````````过三角形ABC的顶点C作一条直线与边AB及中线AD分别交于点E和F.过D做DM平行FC交AB于M,说明AE*FB*=2AF*ED
三角形FBC中,D是中点,FC//MD,所以DM为三角形FBC的中位线,FM=BM
BM/FB=1/2
BM=1/2FB=FM
三角形ADM中,FE//MD,有
AE/ED=AF/FM=AF/1/2FB
即AE/ED=2AF/FB
所以
AE*FB*=2AF*ED