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Found problems: 1

2022 Sharygin Geometry Olympiad, 10.8
Tags: geometry , 3D geometry , octahedron , Torricelli Point
Let $ABCA'B'C'$ be a centrosymmetric octahedron (vertices $A$ and $A'$, $B$ and $B'$, $C$ and $C'$ are opposite) such that the sums of four planar angles equal $240^o$ for each vertex. The Torricelli points $T_1$ and $T_2$ of triangles $ABC$ and $A'BC$ are marked. Prove that the distances from $T_1$ and $T_2$ to $BC$ are equal.