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USAMO 1983 Problem 4 - Constructing altitude of terahedron

Source: USAMO 1983 Problem 4

August 16, 2011
AMCUSA(J)MOUSAMOgeometry3D geometrytetrahedrongeometry unsolved

Problem Statement

Six segments S1,S2,S3,S4,S5,S_1, S_2, S_3, S_4, S_5, and S6S_6 are given in a plane. These are congruent to the edges AB,AC,AD,BC,BD,AB, AC, AD, BC, BD, and CDCD, respectively, of a tetrahedron ABCDABCD. Show how to construct a segment congruent to the altitude of the tetrahedron from vertex AA with straight-edge and compasses.
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