MathNet 2022-part-06 — 196 problems (EN–VI) Question 38

Let $ABCDEF$ be a hexagon and let $M, N, P, Q, R, S$ be the midpoints of $AB$, $BC$, $CD$, $DE$, $EF$, and $FA$, respectively. Show that $MQ \perp PS$ if and only if $RN^{2} = MQ^{2} + PS^{2}$.