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Ratio of projections of a tetrahedron on two planes.

Source:

March 17, 2011
ratiogeometry3D geometrytetrahedron

Problem Statement

Prove that for any tetrahedron in space, it is possible to find two perpendicular planes such that ratio between the projections of the tetrahedron on the two planes lies in the interval [12,2].[\frac{1}{\sqrt{2}}, \sqrt{2}].