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Tetrahedron and sphere - TT 2009 Senior-A3

Source:

September 3, 2010
geometry3D geometrytetrahedronspheregeometry unsolved

Problem Statement

Every edge of a tetrahedron is tangent to a given sphere. Prove that the three line segments joining the points of tangency of the three pairs of opposite edges of the tetrahedron are concurrent.
(7 points)