Does anyone know a good method that I can use to build a poincare line segment in The Geometer's Sketchpad? I can build a ray and a line tool no problem but my ray's either disappear or "loop around". Problem 14.2.3 gives you two hints for building a ray tool and I used the second method to build a "reliable" ray by finding inversion points for $B$ and creating an arc through three points. Then finding the intersection of the poincare disk and the arc, hiding the first line I created and then creating another arc through $A$, $B$ and the intersection point on the circle.
I tried using that same method to create a line segment tool, but the line segment falls apart if I try and move any of the points around. I can move the ray around and it is very reliable.