MathNet 2017-part-07 — 172 problems (EN–VI) Question 31

Let $ABCD$ be a convex quadrilateral with $AC = 7$ and $BD = 17$. Let $M, P, N, Q$ be the midpoints of sides $AB$, $BC$, $CD$, $DA$ respectively. Compute $MN^{2} + PQ^{2}$.