SHARYGIN 2016 Problem 23
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)
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.
Similar problems
These problems have the most words in common with this statement.