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MMO 271 Moscow MO 1954 AB=CD=8, AC=BD=10, AD=BC=13 in space

Source:

August 13, 2019
3D geometrydistancegeometrygeometric inequality

Problem Statement

Do there exist points A,B,C,DA, B, C, D in space, such that AB=CD=8,AC=BD=10AB = CD = 8, AC = BD = 10, and AD=BC=13AD = BC = 13?
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