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The lines drawn to the Vertices of a face of a Tetrahedron from the point of contact of the Face with the Insphere form three Angles at the point of contact which are the same three Angles in each Face.
References
Brown, B. H. ``Theorem of Bang. Isosceles Tetrahedra.'' Amer. Math. Monthly 33, 224-226, 1926.
Honsberger, R. Mathematical Gems II. Washington, DC: Math. Assoc. Amer., p. 93, 1976.