can segments of tangents of sphere circumscribed on 4dron, form triangle?
Source: Sharygin Geometry Olympiad 2016 First Round P23 grades 10-11
July 25, 2018
geometry3D geometrysphere
Problem Statement
A sphere touches all edges of a tetrahedron. Let and d be the segments of the tangents to the sphere from the vertices of the tetrahedron. Is it true that that some of these segments necessarily form a triangle? (It is not obligatory to use all segments. The side of the triangle can be formed by two segments)