Triangle $ABC$ is right angled at $A$.Let $D$ be a point on $BC$.
$E$ and $F$ are reflections of $D$ on $AC$ and $AB$ respectively.
Prove that $[ABC]\geq [DEF]$.Find all position of $D$ for equality
(Here $[x]$ denotes the area of $x$).
BdMO National Secondary 2010#8
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