The Hidden Twin of Morley's Five Circles Theorem

We give an algebraic proof of a slightly extended version of Morley's Five Circles Theorem. The theorem holds in all Miquelian Mobius planes obtained from a separable quadratic field extension, in particular in the classical real Mobius plane. Moreover, the calculations bring to light a hidden twin of the Five Circles Theorem that seems to have been overlooked until now.

Automated summary

This article provides an algebraic proof of a slightly extended version of Morley's Five Circles Theorem. The theorem holds in all Miquelian Mobius planes obtained from a separable quadratic field extension, particularly in the classical real Mobius plane. Furthermore, the calculations reveal a hidden twin theorem of the Five Circles Theorem that has apparently been overlooked until now.