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 no 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 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).