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RU-ALLRUSSIAN 1983 Problem 19

    Interior points D, E, F are chosen on the sides BC, CA, AB (not at the vertices). Let k be the length of the longest side of DEF. Let a, b, c be the lengths of the longest sides of AFE, BDF, CDE respectively. Show that k≥3\mathrm{k}\geq \sqrt{3} min(a, b, c) /2. When do we have equality?

    Dataset text NuminaMath olympiads. Quoted with source.

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