English

A theorem on circle configurations

History and Overview 2007-06-07 v2

Abstract

A formula for the radii and positions of four circles in the plane for an arbitrary linearly independent circle configuration is found. Among special cases is the recent extended Descartes Theorem on the Descartes configuration and an analytic solution to the Apollonian problem. The general theorem for n-spheres is also considered.

Keywords

Cite

@article{arxiv.0706.0372,
  title  = {A theorem on circle configurations},
  author = {Jerzy Kocik},
  journal= {arXiv preprint arXiv:0706.0372},
  year   = {2007}
}
R2 v1 2026-06-21T08:34:44.972Z