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Let A B C be an isosceles triangle wit...

Let `A B C` be an isosceles triangle with `A B=A C` and let `D ,\ E ,\ F` be the mid points of `B C ,\ C A\ a n d\ A B` respectively. Show that `A D_|_F E\ a n d\ A D` is bisected by `F E`

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Since D,E and F are the mid-points of sides BC,CA and AB respectively.
`AFDE` is a parallelogram
`=>AF=DE \and\ AE=DF`
`=>1/2AB=DE`
`1/2 AC=DF`
`DF=DF` (AB=AC
`=>AE=AF=DE=DF`
`=>AEDF` is a rhombus
AD and FE bisect each other at the right angle.
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