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: 2

2019 Jozsef Wildt International Math Competition, W. 67
Denote $T$ the Toricelli point of the triangle $ABC$. Prove that $$AB^2 \times BC^2 \times CA^2 \geq 3(TA^2\times TB + TB^2 \times TC + TC^2 \times TA)(TA\times TB^2 + TB \times TC^2 + TC \times TA^2)$$
inequalities geometric inequality geometry toricelli point geometric inequalities

2022 Sharygin Geometry Olympiad, 10.8
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.
octahedron geometry 3d geometry toricelli point solid geometry