Problem

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

Tags: geometry, circumcircle, orthocenter, Pure geometry



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


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