IMO 1984 LL USS65

A tetrahedron is inscribed in a sphere of radius 1 such that the

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IMO 1984 LL USS65

Origin: USS

Problem

A tetrahedron is inscribed in a sphere of radius 1 such that the center of the sphere is inside the tetrahedron. Prove that the sum of lengths of all edges of the tetrahedron is greater than 6.