prove triangles obtained by the transpositions of vertices are identical
Source: Sharygin Finals 2023 10.7
August 2, 2023
geometrySharygin Geometry OlympiadSharygin 2023
Problem Statement
There are points in the space: yellow and red. Any four of them are not coplanar. May the number of triangles with red vertices hooked with the triangle with yellow vertices be equal to ? Yellow triangle is hooked with the red one if the boundary of the red triangle meet the part of the plane bounded by the yellow triangle at the unique point. The triangles obtained by the transpositions of vertices are identical.