MathNet 2017-part-05 — 176 problems (EN–VI) Question 34

Let $M$ be the midpoint of the side $[AB]$ of the square $ABCD$, let $P$ be the projection of $B$ on $CM$ and let $N$ be the midpoint of the segment $[CP]$. The bisector of the angle $DAN$ meets line $DP$ in $Q$. Show that the quadrilateral $BMQN$ is a parallelogram.

Adrian Bud