IMO Shortlist 1972 problem 5


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2. travnja 2012.
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Prove the following assertion: The four altitudes of a tetrahedron ABCD intersect in a point if and only if
AB^2 + CD^2 = BC^2 + AD^2 = CA^2 + BD^2.
Izvor: Međunarodna matematička olimpijada, shortlist 1972