This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2023 Baltic Way, 14
Tags: geometry , orthogonalaty , centroid
Let $ABC$ be a triangle with centroid $G$. Let $D, E, F$ be the circumcenters of triangles $BCG, CAG, ABG$. Let $X$ be the intersection of the perpendiculars from $E$ to $AB$ and from $F$ to $AC$. Prove that $DX$ bisects $EF$.