1965 IMO Problems/Problem 6

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.


See Also

1965 IMO (Problems) • Resources
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Problem 5
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