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orthocenter, intersection of 2 circles, 2 midpoints of arcs, are concyclic

Source: Turkey JBMO TST 2018 p3

September 16, 2018
geometryConcyclicarc midpointcircles

Problem Statement

Let HH be the orthocenter of an acute angled triangle ABCABC. Circumcircle of the triangle ABCABC and the circle of diameter [AH][AH] intersect at point EE, different from AA. Let MM be the midpoint of the small arc BCBC of the circumcircle of the triangle ABCABC and let NN the midpoint of the large arc BCBC of the circumcircle of the triangle BHCBHC Prove that points E,H,M,NE, H, M, N are concyclic.
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