BALKAN 1996 Problem 3

In a convex pentagon $ABCDE$ , the points $M$ , $N$ , $P$ , $Q$ , $R$ are the midpoints of the sides $AB$ , $BC$ , $CD$ , $DE$ , $EA$ , respectively. If the segments $AP$ , $BQ$ , $CR$ and $DM$ pass through a single point, prove that $EN$ contains that point as well.

Yugoslavia