MathNet 2017-part-07 — 172 problems (EN–VI) Question 19

Let $ABCD$ be a convex quadrilateral with $AB = 5$, $BC = 6$, $CD = 7$, and $DA = 8$. Let $M$, $P$, $N$, $Q$ be the midpoints of sides $AB$, $BC$, $CD$, $DA$ respectively. Compute $MN^{2} - PQ^{2}$.