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Problem with circumcenters and orthocenter

Source: Romania National Olympiad 2016, grade ix, p.1

August 23, 2019
geometrycircumcircleorthocenterPure geometry

Problem Statement

The orthocenter H H of a triangle ABC ABC is distinct from its vertices and its circumcenter O. O. M,N,P M,N,P are the circumcenters of the triangles HBC,HCA, HBC,HCA, respectively, HAB. HAB. Prove that AM,BN,CP AM,BN,CP and OH OH are concurrent.
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