A well-known result of the Euclidean planimetry says that the heights of any triangle have a common point called the *orthocentre* of the triangle. This results is not true in the Neutral Geometry because the heights of an obtuse triangle need not intersect. Nonetheless any two heights of an acute triangle (= a triangle whose all angles are acute) do intersect, by the Pasch Axiom. 

>**Problem.** Is it true that the heights of any acute triangle have a common point (in the Neutral Geometry)?

**Remark.** The answer to the problem is affirmative if the acute triangle is a midpoint triangle of another triangle, see Proposition 9.7 in [these lecture notes][1] of Polly Knight. But in the Hyperbolic Geometry an acute triangle (even equlateral) needs not be a midpoint triangle of another triangle. In that case what does happen with the intersecting points of the heights of an acute triangle? Do they coincide? Since this is rather a basic question in the Neutral Geometry, I hope that an answer is known (to specialists). In the footnote 32 to *Remark* after [Proposition 9.7][1], Polly Knight writes that in the Klein's model the heights of an acute triangle indeed have a common point. But the Neutral Geometry has many other models, in particular, non-Archimedean models and even models in which the sum of a triangle is larger than $\pi$. In the mentioned footnote 32 Polly Knight writes that ''a proof in *neutral* geometry is certainly valid a real bottle of wine''. So, is such a proof (worth a ``real bottle of wine'') known?  


  [1]: https://silo.tips/download/9-neutral-triangle-geometry