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Conclusion
The primary focus of this paper has been on the construction of custom
tools in GeoGebra for creating hyperbolic lines and hyperbolic circles
in the Poincaré disk model. The hyperbolic line tool is robust and works
well in all cases including when points A and B are in the
interior of γ, on the boundary of γ and when they are on the same
diameter. The hyperbolic circle is similarly robust and works for the
full range of positions of the center point A and point B
within and on γ. Tools for creating hyperbolic segments and rays can be
constructed in a manner similar to that of hyperbolic lines with some
modifications. If the reader wishes to create a more complete suite of
tools for working with the Poincaré disk, then it is worth noting that
the construction of hyperbolic perpendicular bisectors, hyperbolic
midpoints, hyperbolic perpendicular lines and hyperbolic angle bisectors
mimic their corresponding Euclidean compass and straightedge
constructions.