Below is an applet with drawing tools for the Poincaré Disk model of
hyperbolic geometry.
(Be patient; the applet takes a few seconds to load.)
Use the "disk" menu (2nd tool from the right) to access the tools of
hyperbolic geometry in this model.
Use the File menu (upper right) to download an image of your work.
(You can also save your work as a .ggb file that you can use with other
installations of installation
of GeoGebra.)
Acknowledgment: The underlying applet Poincare.ggb was found online in 2016, authorship unknown.