RMO 2018 K5

In a cyclic quadrilateral $ABCD$ with circumcenter $O$ , the diagonals $AC$ and $BD$ intersect at $X$ . Let the circumcircles of triangles $AXD$ and $BXC$ intersect at $Y$ . Let the circumcircles of triangles $AXB$ and $CXD$ intersect at $Z$ . If $O$ lies inside $ABCD$ and if the points $O,X,Y,Z$ are all distinct, prove that $O,X,Y,Z$ lie on a circle.