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volume of tetrahedron ineq

Source: Polish MO Finals 1981 p6

August 24, 2024
geometry3D geometrytetrahedronGeometric Inequalities

Problem Statement

In a tetrahedron of volume VV the sum of the squares of the lengths of its edges equals SS. Prove that V≤SS723V \le \frac{S\sqrt{S}}{72\sqrt{3}}
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