BALKAN 2000 Problem 2

Let $ABC$ be an acute-angled triangle and $D$ the midpoint of $BC$ . Let $E$ be a point on segment $AD$ and $M$ its projection on $BC$ . If $N$ and $P$ are the projections of $M$ on $AB$ and $AC$ then the interior angule bisectors of $\angle NMP$ and $\angle NEP$ are parallel.