I am making a slow inroad into a comparison between GeoGebra and the TI Nspire . I have previously blogged about the capability to plot polar graphs using just basic geometry (see here for an example.)
It will be a while before I get up to speed, but in the meantime I will proceed just as I did at first using Geogebra: generating an animated gif. Any interactivity in my blog may come much later (that is, if TI has allowed for actively embedding documents.)
In the meantime, it's a start! Here two points are rotating in opposite directions, one twice as fast as the other, and the midpoint between them is traced.