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Max value for min distance

Source: Germany final round grade 12-13, 2006, Crux mathematicorum

December 1, 2015
geometry3D geometrysphere

Problem Statement

Five points are on the surface of of a sphere of radius 11. Let amina_{\text{min}} denote the smallest distance (measured along a straight line in space) between any two of these points. What is the maximum value for amina_{\text{min}}, taken over all arrangements of the five points?
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