Yu-Dong Wu and Zhi-Hua Zhang, The edge-tangent sphere of a circumscriptible tetrahedron,
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.

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