Circle incidence theorems

TL;DR

This paper generalizes a notable concurrency theorem involving circles and radical axes from pentagrams to n-gons, expanding the understanding of circle incidences in polygonal configurations.

Contribution

It extends Hoehn's circle incidence theorem from pentagrams to arbitrary n-gons, providing a broader geometric framework.

Findings

Radical axes of consecutive circles are concurrent or parallel in the generalized setting.

The theorem applies to polygons with any number of sides, not just pentagons.

The result unifies and extends known circle incidence properties in polygon geometry.

Abstract

Larry Hoehn discovered a remarkable concurrence theorem about pentagrams. Draw cicles through two consecutive vertices and the intersection points of the sides in between, Then the radical axes of each pair of consecutive circles are concurrent or parallel. In this note we prove a generalisation to n-gons.