Regional problem · Geometry

Let \(H\) be the orthocenter of a triangle \(ABC\), and let \(K\) be the point symmetric to \(H\) with respect to the midpoint of the side \(BC\). Prove that \(AK\) is a diameter of the circumcircle of the triangle \(ABC\).

\(M\) is the midpoint of \(BC\) and \(K\) is the reflection of \(H\) in \(M\).

Serbian Regional Competition 2012, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source

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