Mathematica competitions in Croatia

Let $ABC$ be an acute triangle such that $|AC|>|BC|$. Let $H$ be the orthocentre of that triangle, $N$ the foot of the altitude from $B$, and $P$ the midpoint of the side $AB$. The circumcircles of the triangles $ABC$ and $CHN$ intersect in $C$ and $D$. Prove that the points $B,D,N$ and $P$ lie on the same circle.