A contemporary inversive geometry solution of the three-circle problem of Steiner

TL;DR

This paper provides a modern, inversive geometry-based solution to Steiner's three-circle problem, which involves constructing a circle intersecting three given circles at specified angles, offering a concise and self-contained approach.

Contribution

It introduces a new, concise inversive geometry method for solving Steiner's three-circle problem, enhancing understanding and solution techniques.

Findings

Successful derivation of a self-contained solution

Simplification of the construction process

Potential applications in geometric design

Abstract

We present a concise self-contained inversive geometry solution of the three-circle problem of Steiner of constructing a circle that intersects each of the three given circles at one of the three given angles.