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RU-ALLRUSSIAN 1982 Problem 8

    M is a point inside a regular tetrahedron. Show that we can find two vertices A, B of the tetrahedron such that cos⁡AMB≤−1/3\cos \mathrm{AMB} \leq - 1 / 3 .

    Dataset text NuminaMath olympiads. Quoted with source.

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