Question 53
The diagonals of the convex quadrilateral $ABCD$ are perpendicular and meet in $O$. The perpendicular to $(AB)$ passing through $O$ meets $(AB)$ in $M$ and $(CD)$ en $M'$. The perpendicular to $(BC)$ passing through $O$ meets $(BC)$ in $N$ and $(DA)$ en $N'$. The perpendicular to $(CD)$ passing through $O$ meets $(CD)$ in $P$ and $(AB)$ en $P'$. The perpendicular to $(DA)$ passing through $O$ meets $(DA)$ in $Q$ and $(BC)$ en $Q'$. Prove that $M, N, P, Q, M', N', P', Q'$ points are cocyclic.