Points and Lines Configurations for Perpendicular Bisectors of Convex Cyclic Polygons

Abstract

We characterize the topological configurations of points and lines that may arise when placing $n$ points on a circle and drawing the $n$ perpendicular bisectors of the sides of the corresponding convex cyclic $n$-gon. We also provide exact and asymptotic formulas describing a random realizable configuration, obtained either by sampling the points uniformly at random on the circle or by sampling a realizable configuration uniformly at random.