AoPS - Problem

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Problem

Source: IMO LongList 1967, Great Britain 3

Tags: geometry, point set, euclidean distance, maximization, IMO Shortlist, IMO Longlist

orl

16.12.2004 20:05

The $n$ points $P_1,P_2, \ldots, P_n$ are placed inside or on the boundary of a disk of radius 1 in such a way that the minimum distance $D_n$ between any two of these points has its largest possible value $D_n.$ Calculate $D_n$ for $n = 2$ to 7. and justify your answer.