Five edges of a tetrahedron are tangent to a sphere. Prove that there are another five edges from this tetrahedron that are also tangent to a $($not necessarily the same$)$ sphere.
Source: 239-School Open Olympiad (Senior Level)
Tags: 3D geometry, Spheres, geometry
Five edges of a tetrahedron are tangent to a sphere. Prove that there are another five edges from this tetrahedron that are also tangent to a $($not necessarily the same$)$ sphere.