KöMaL 2019 C1572

In a trapezium $ABCD$, let $M$ denote the intersection of diagonals $AC$ and $BD$, and let $N$ and $P$ denote the centres of the circumscribed circles of triangles $ABC$ and $ACD$, respectively. Prove that $M$, $N$ and $P$ are collinear if and only if $ABCD$ is a parallelogram or a cyclic trapezium.