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1965 IMO Problems/Problem 6

Revision as of 10:45, 16 July 2009 by Xpmath (talk | contribs) (Created page with '== Problem == In a plane a set of <math>n</math> points (<math>n\geq 3</math>) is given. Each pair of points is connected by a segment. Let <math>d</math> be the length of the lo…')
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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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