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MMO 251 Moscow MO 1953 2 groups of convex polygons from 16 concyclic points

Source:

August 9, 2019
pointscircleconvex polygoncombinatorial geometry

Problem Statement

On a circle, distinct points A1,...,A16A_1, ... , A_{16} are chosen. Consider all possible convex polygons all of whose vertices are among A1,...,A16A_1, ... , A_{16} . These polygons are divided into 22 groups, the first group comprising all polygons with A1A_1 as a vertex, the second group comprising the remaining polygons. Which group is more numerous?
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