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any 3 out of 6 segments form a triangle, what about a tetrahedron?

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p2

October 20, 2020
geometry3D geometrytetrahedrontriangle inequality

Problem Statement

Six segments are such that any three can form a triangle. Is it true that these segments can be used to form a tetrahedron?
(S. Markelov)