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1965 IMO Problems/Problem 6

Revision as of 18:14, 17 May 2020 by Olivera (talk | contribs) (After user awe-sum solved the problem, I linked their image of the problem solution because I couldn't do the asymptote for it.)

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

Image of problem Solution. Credits to user awe-sum.


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