MathDB
Tetrahedron

Source: Czech and Slovak Olympiad 1967, National Round, Problem 2

July 1, 2024
geometry3D geometrytetrahedronacuteTriangle

Problem Statement

Let ABCDABCD be a tetrahedron such that AB2+CD2=AC2+BD2=AD2+BC2.AB^2+CD^2=AC^2+BD^2=AD^2+BC^2. Show that at least one of its faces is an acute triangle.
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