Points in space with distinct distances form certain triangles
Source: Bundeswettbewerb Mathematik 2018, Round 1 - #4
June 30, 2018
geometrycombinatorics3D geometryTriangledistance
Problem Statement
We are given six points in space with distinct distances, no three of them collinear. Consider all triangles with vertices among these points.Show that among these triangles there is one such that its longest side is the shortest side in one of the other triangles.