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Sphere tangent to a tetrahedron

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September 15, 2010
geometry3D geometryspheretetrahedronIMO Shortlist

Problem Statement

A sphere SS is tangent to the edges AB,BC,CD,DAAB,BC,CD,DA of a tetrahedron ABCDABCD at the points E,F,G,HE,F,G,H respectively. The points E,F,G,HE,F,G,H are the vertices of a square. Prove that if the sphere is tangent to the edge ACAC, then it is also tangent to the edge BD.BD.
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