1965 IMO Problems/Problem 6

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Problem

In a plane a set of $n$ points ( $n\geq 3$ ) is given. 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 $n$ .

Solution

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1965 IMO Problems/Problem 6

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Problem

Solution