Yu-Dong Wu and Zhi-Hua Zhang, The edge-tangent sphere of a circumscriptible
Forum Geometricorum, 7 (2007) 19--24.
Abstract: A tetrahedron is circumscriptible if there is a sphere tangent
to each of its six edges. We prove that the radius l of the edge-tangent
sphere is at least \sqrt 3 times the radius of its inscribed sphere. This
settles affirmatively a problem posed by Z. C. Lin and H. F. Zhu. We
also briefly examine the generalization into higher dimension, and
pose an analogous problem for an n-dimensional simplex admitting a
sphere tangent to each of its edges.