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Prove that the lines $AM, BN, CP$ and $OH$ are concurrent.

Source: Moldova EGMO TST 2021

February 4, 2023
geometrycircumcircle

Problem Statement

A triangle ABCABC has the orthocenter HH different from the vertexes and the circumcenter OO. Let M,NM, N and PP be the circumcenters of triangles HBC,HCAHBC, HCA and HABHAB. Prove that the lines AM,BN,CPAM, BN, CP and OHOH are concurrent.
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