IR-TST 2011 Problem 1

In acute triangle $ABC$ angle $B$ is greater than $C$ . Let $M$ is midpoint of $BC$ . $D$ and $E$ are the feet of the altitude from $C$ and $B$ respectively. $K$ and $L$ are midpoint of $ME$ and $MD$ respectively. If $KL$ intersect the line through $A$ parallel to $BC$ in $T$ , prove that $TA=TM$ .