On Ceva's and Menelaus's Theorems for a Möbius triangle
arXiv:2605.29905
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 Möbius triangle we define the incenter, excenters, and orthocenter.
35 pages, 18 figures