A triangle $ABC$ has the orthocenter $H$ different from the vertexes and the circumcenter $O$. Let $M, N$ and $P$ be the circumcenters of triangles $HBC, HCA$ and $HAB$. Prove that the lines $AM, BN, CP$ and $OH$ are concurrent.
Source: Moldova EGMO TST 2021
Tags: geometry, circumcircle
A triangle $ABC$ has the orthocenter $H$ different from the vertexes and the circumcenter $O$. Let $M, N$ and $P$ be the circumcenters of triangles $HBC, HCA$ and $HAB$. Prove that the lines $AM, BN, CP$ and $OH$ are concurrent.