MathDB

24

Part of 1989 IMO Shortlist

Problems(1)

Configurations for which this maximum is attained

Source: IMO Longlist 1989, Problem 74

9/18/2008
For points A1,…,A5 A_1, \ldots ,A_5 on the sphere of radius 1, what is the maximum value that min1≤i,j≤5AiAj min_{1 \leq i,j \leq 5} A_iA_j can take? Determine all configurations for which this maximum is attained. (Or: determine the diameter of any set {A1,…,A5} \{A_1, \ldots ,A_5\} for which this maximum is attained.)
geometry3D geometryspherecombinatoricsmaximizationgeometric inequalityIMO Shortlist