MathDB
combinatorial geometry

Source: Yugoslav TST 1974 P3

May 29, 2021
combinatorial geometrycombinatoricsgeometry

Problem Statement

Let SS be a set of nn points P1,P2,…,PnP_1,P_2,\ldots,P_n in a plane such that no three of the points are collinear. Let α\alpha be the smallest of the angles ∠PiPjPk\angle P_iP_jP_k (i≠j≠k≠i,i,j,k∈{1,2,…,n}i\ne j\ne k\ne i,i,j,k\in\{1,2,\ldots,n\}). Find max⁡Sα\max_S\alpha and determine those sets SS for which this maximal value is attained.
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