A note on the centers of a closed chain of circles

TL;DR

This paper proves that the centers of a closed chain of circles, each tangent to the next at points on two fixed circles, form a tangent polygon of a conic, revealing a geometric property of such circle chains.

Contribution

It establishes a new geometric relationship between circle chains and conic tangent polygons, expanding understanding of circle configurations.

Findings

Centers form a tangent polygon of a conic

Circle chain configuration relates to conic tangency

Provides a geometric proof of the relationship

Abstract

In this note we prove that the centers of a closed chain of circles for which every two consecutive members meet in the points of two given circles form a tangent polygon of a conic.