3.1 Diameters
If A and B are collinear with O, then the hyperbolic line passing through A and B is a diameter of γ. Although diameters are simple in theory, there are some complications when implementing this case in GeoGebra since in the end all three cases will be combined into a single custom tool. In an ideal world, we could use the Segment[ <Point>, <Point> ] command to construct the diameter. Unfortunately, the If[ <Condition>, <Then>, <Else> ] command needed to combine the cases requires that the <Then> and <Else> objects be of the same type. Since segments and arcs do not meet this criterion, the diameter will be approximated using the small arc of a large circle as shown in Figure 5.