No \(4\)-Isosceles Set with Eight Points on a Circle

Abstract

A finite planar set is \(k\)-isosceles for \(k \geq 3\) if every \(k\)-point subset of the set contains a point equidistant from two others. There exists no convex \(4\)-isosceles \(8\)-point set with \(8\) points on a circle.