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all faces acute in tetrahedron with AB = CD , AC = BD, AD = BC

Source: Polish MO Second Round 1973 p5

September 8, 2024
geometry3D geometrytetrahedron

Problem Statement

Prove that if in the tetrahedron ABCD ABCD we have AB=CD AB = CD , AC=BD AC = BD , AD=BC AD = BC , then all faces of the tetrahedron are acute-angled triangles.
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