Is the hyperbolic version of [Sylvester co linear problem](https://en.wikipedia.org/wiki/Sylvester%E2%80%93Gallai_theorem)  true?



Hyperbolic version of Sylvester co-linear problem
Yes. Use the projective (Cayley-Klein) model of the hyperbolic plane. Your points lie inside a disk. Hyperbolic lines are chords of that disk. Since the Euclidean Silvester-Gallai is true, you have the same conclusion in the hyperbolic case.


