MathDB

3

Part of 2018 JBMO TST-Turkey

Problems(1)

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

Source: Turkey JBMO TST 2018 p3

9/16/2018
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.
geometryConcyclicarc midpointcircles