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Maximal length in a varying tetrahedron

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October 31, 2010
geometry3D geometrytetrahedronspheregeometry unsolved

Problem Statement

A variable tetrahedron ABCDABCD has the following properties: Its edge lengths can change as well as its vertices, but the opposite edges remain equal (BC=DA,CA=DB,AB=DC)(BC = DA, CA = DB, AB = DC); and the vertices A,B,CA,B,C lie respectively on three fixed spheres with the same center PP and radii 3,4,123, 4, 12. What is the maximal length of PDPD?
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