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Existence of tetrahedron

Source: Czech and Slovak Olympiad 1978, National Round, Problem 4

October 11, 2024
geometry3D geometrytetrahedronVolume

Problem Statement

Is there a tetrahedron ABCDABCD such that AB+BC+CD+DA=12 cmAB+BC+CD+DA=12\text{ cm} with volume V≥23 cm3?\mathrm V\ge2\sqrt3\text{ cm}^3?
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