IMO Shortlist 1965 problem 6

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Dodao/la: arhiva
2. travnja 2012.
In a plane a set of n points (n \geq 3) is give. Each pair of points is connected by a segment. Let d be the length of the longest of these segments. We define a diameter of the set to be any connecting segment of length d. Prove that the number of diameters of the given set is at most n.
Izvor: Međunarodna matematička olimpijada, shortlist 1965