English

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.

Keywords

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}
}