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Minimal sum of distances in a tetrahedron

Source: Austrian Federal Competition for Advanced Students 2011, #4

May 15, 2011
geometry3D geometrytetrahedronfunctiongeometry proposed

Problem Statement

Inside or on the faces of a tetrahedron with five edges of length 22 and one edge of lenght 11, there is a point PP having distances a,b,c,da, b, c, d to the four faces of the tetrahedron. Determine the locus of all points PP such that a+b+c+da+b+c+d is minimal and the locus of all points PP such that a+b+c+da+b+c+d is maximal.
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