HK-PC 2018 Problem 6

A triangle $ABC$ has its orthocentre $H$ distinct from its vertices and from the circumcenter $O$ of $\triangle ABC$ . Denote by $M, N$ and $P$ respectively the circumcenters of triangles $HBC, HCA$ and $HAB$ . Show that the lines $AM, BN, CP$ and $OH$ are concurrent.