IMO Shortlist 1965 problem 6
Dodao/la: arhiva2. travnja 2012.
In a plane a set of
) is give. Each pair of points is connected by a segment. Let
be the length of the longest of these segments. We define a diameter of the set to be any connecting segment of length
. Prove that the number of diameters of the given set is at most
Izvor: Međunarodna matematička olimpijada, shortlist 1965