MathNet 2017-part-02 — 176 problems (EN–VI) Question 137

Let $ABC$ be a triangle whose orthocentre $H$ is distinct from the vertices and from the circumcentre $O$. Denote by $M, N, P$ the circumcentres of the triangles $HBC$, $HCA$ and $HAB$.

Show that the lines $(AM)$, $(BN)$, $(CP)$ and $(OH)$ are concurrent.