Angle Bisectors (hyperbolic)
Here lies the same construction as the previous theorem, although in this case we examine the situation in terms of hyperbolic geometry. Notice many similarities between this construction and the previous construction. The intersection, F, lies within the boundaries. We can move the points as we see fit and that point will never leave these boundaries. Go for it!
See the previous example for theorem and proof, as both work in hyperbolic geometry.