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Tetrahedron

Source: Vietnam NMO 1962 Problem 3

February 1, 2009
geometry3D geometrytetrahedrongeometry unsolved

Problem Statement

Let ABCD ABCD is a tetrahedron. Denote by A′ A', B′ B' the feet of the perpendiculars from A A and B B, respectively to the opposite faces. Show that AA′ AA' and BB′ BB' intersect if and only if AB AB is perpendicular to CD CD. Do they intersect if AC \equal{} AD \equal{} BC \equal{} BD?
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