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RU-ALLRUSSIAN 1986 Problem 14

    Two points A and B are inside a convex 12- gon. Show that if the sum of the distances from A to each vertex is a and the sum of the distances from B to each vertex is b, then la−bl<10\mathrm{la} - \mathrm{bl} < 10 |AB|.

    Dataset text NuminaMath olympiads. Quoted with source.

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