KöMaL problem A, 2026

Geometry Difficulty 8.0 Shortlist Prove it Hungary

Let $ABC$ be an acute triangle with orthocenter $H$ . Points $D$ and $E$ lie on the lines $AC$ and $AB$ , respectively, such that the points $B$ , $C$ , $D$ , $E$ are concyclic, and the line $DE$ bisects the side $BC$ . Suppose that the lines $BD$ and $CE$ meet at $M$ . Prove that the line $HM$ is perpendicular to the symmedian through $A$ .

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