On Ceva's and Menelaus's Theorems for a M\"obius triangle
math.MG2026-05v1license
Abstract
We generalize the classical Ceva's and Menelaus's theorems to curvilinear triangles bounded by circular arcs. We introduce trilinear coordinates associated with such triangles and develop several geometric constructions. In particular, for any proper M\"obius triangle we define the incenter, excenters, and orthocenter.
Comments: 35 pages, 18 figures
Cite
@article{arxiv.2605.29905,
title = {On Ceva's and Menelaus's Theorems for a M\"obius triangle},
author = {Ivan Livinsky},
journal= {arXiv preprint arXiv:2605.29905},
year = {2026}
}