KöMaL problem A, 2024

Geometry Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $ABC$ be an acute triangle. Points $B'$ and $C'$ are located on the interior of sides $AB$ and $AC$ , respectively. Let $M$ denote the second intersection of the circumcircles of triangles $ABC$ and $AB'C'$ , while let $N$ denote the second intersection of the circumcircles of triangles $ABC'$ and $AB'C$ . Reflect $M$ across lines $AB$ and $AC$ , and let $l$ denote the line through the reflections.

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