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Altitudes of a tetrahedron intersect if and only if

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September 22, 2010
geometry3D geometrytetrahedronaltitudesIMO Shortlist

Problem Statement

Prove the following assertion: The four altitudes of a tetrahedron ABCDABCD intersect in a point if and only if AB2+CD2=BC2+AD2=CA2+BD2.AB^2 + CD^2 = BC^2 + AD^2 = CA^2 + BD^2.
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