Tangent Circles on a Number Line

Simon Gregg, up to his usual tricks, is introducing fractions together with Ford circles, inspired by this Numberphile video with Francis Bonahon. Before moving on to the Ford circles (or as a special case), I got interested in the tangents to the 0 and 1 circles. This sketch lets you see the radii in terms of the location, or use a slidable circle, or use the extra tool to make lots of circles. Thanks to Simon, Meagan Mutchmore, and Graeme Anshaw for great Twitter math talk!