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centrosymmetric octahedron and Torricelli points,

Source: Sharygin Finals 2022 10.8

October 26, 2022

geometry3D geometryoctahedronTorricelli Point

Problem Statement

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

BC

are equal.