Proof of the Generalization of the Sawayama-Th\'ebault Theorem
Metric Geometry
2026-03-20 v1
Abstract
We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for resolving the problem.
Cite
@article{arxiv.2603.18651,
title = {Proof of the Generalization of the Sawayama-Th\'ebault Theorem},
author = {Miłosz Płatek},
journal= {arXiv preprint arXiv:2603.18651},
year = {2026}
}