Question 41
Consider a convex quadrilateral $\mathcal P$ and a point $X$ in its interior. Let $M,N,P,Q$ be the orthogonal projections of $X$ onto its four sides. Suppose that $M,N,P,Q$ lie on a circle with center $L$. Prove that $L$ and the midpoints $J,K$ of the diagonals of $\mathcal P$ are collinear.