On Ceva's and Menelaus's Theorems for a M\"obius triangle
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cevamenelausobiustheoremstriangletrianglesarcsassociated
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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.
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