Constructing the circumcircle of a hyperbolic triangle in the Poincare disk

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Now use your hyperbolic ruler and compass tools to construct the circumcentre and circumcircle of a hyperbolic triangle.
Note. The circumcentre should be the hyperbolic centre of the circle, i.e. the hyperbolic distance from the circumcentre to each vertex of the triangle is the same.
The picture below contains an example of a hyperbolic triangle PQR with hyperbolic circumcentre S. Once you have found S then the hyperbolic circle tool can be used to draw the circumcircle. Can you construct the hyperbolic circumcentre and circumcircle of the triangle 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.
Question. Does every set of three points admit a hyperbolic circumcircle in the Poincaré disk?

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