6. [6] Let $A B C D$ be a convex quadrilateral with $A C=7$ and $B D=17$. Let $M, P, N, Q$ be the midpoints of sides $A B, B C, C D, D A$ respectively. Compute $M N^{2}+P Q^{2}$
Answer:
169
$M P N Q$ is a parallelogram whose side lengths are 3.5 and 8.5 so the sum of squares of its diagonals is $\frac{7^{2}+17^{2}}{2}=169$ $\square$