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The max min of angles A_iA_jA_k for 5 points in a plane

Source: APMO 2011

May 18, 2011
geometrygeometric transformationcombinatorics proposedcombinatorics

Problem Statement

Five points A1,A2,A3,A4,A5A_1,A_2,A_3,A_4,A_5 lie on a plane in such a way that no three among them lie on a same straight line. Determine the maximum possible value that the minimum value for the angles ∠AiAjAk\angle A_iA_jA_k can take where i,j,ki, j, k are distinct integers between 11 and 55.
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