Question 69
The quadrilateral $ABCD$ is inscribed in the circle with center $O$, the points $M$ and $N$ are the middle points of the diagonals $[AC]$ and $[BD]$ respectively and $P$ is the intersection point of the diagonals. It is known that the points $O, M, N$ and $P$ are distinct. Prove that the points $O, M, B$ and $D$ are concyclic if and only if the points $O, N, A$ and $C$ are concyclic.