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Macedonian JBMO TST 2014, Problem 2

Source:

March 30, 2015
geometry

Problem Statement

Point MM is an arbitrary point in the plane and let points GG and HH be the intersection points of the tangents from point M and the circle kk. Let OO be the center of the circle kk and let KK be the orthocenter of the triangle MGHMGH. Prove that ∠GMH=∠OGK{\angle}GMH={\angle}OGK.
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