I am trying to learn about finding the angles in hyperbolic geometry and I am trying to understand this example given in Stahl's Introduction to topology and geometry.
You can notice that there is a yellow line, the author mentions that it is clear the euclidean centers of the geodesics $AB$, $AC$ and $BC$ are $P(2,0)$, $Q(4,0)$, and $R(6,0)$. However it is not so clear for me, how did the author obtain these coordinates or atleast one of them?
I suppose the author uses the Poincare half plane model ( https://en.wikipedia.org/wiki/Poincar%C3%A9_half-plane_model )
where hyperbolic lines (geodesics) are half circles centered on the boundary line (x axis) Given that the points are the same distance of the boundary line / x axis there center is halfway the two points on the xaxis.
and this way he gets to the points $P$ $Q$ and $R$
the angles are the angles between the half circles
Hopes this helps
PS i don't own Stahls book so cannot go deper than this