Constructing a hyperbolic angle bisector in the Poincare disk

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Now use your hyperbolic ruler and compass tools to construct a hyperbolic line bisecting the angle between two hyperbolic lines.
The picture below contains an example of a hyperbolic triangle PQR with a hyperbolic line bisecting the angle PQR. Can you construct a hyperbolic line bisecting the angle ABC?
Once again, if you really understand Euclid's construction in Euclidean geometry then you should be able to easily do this in hyperbolic geometry using the hyperbolic line and hyperbolic circle tools that you have already constructed.

To help you get a feel for what the solution should be, there is already a tool for constructing hyperbolic angle bisectors. Try and construct them yourself, using only the other given tools.