Question 116
Let $ABCD$ be a cyclic quadrilateral and let the midpoints of $AB$, $BC$, $CD$ and $DA$ be $K$, $L$, $M$ and $N$, respectively. Let the reflections of the point $M$ with respect to the lines $AD$ and $BC$ be $P$ and $Q$, respectively. Finally the circumcenter of the triangle $KPQ$ be $R$. Prove that $RN = RL$.