Thanks to Kate Nowak, and also to Guillermo Bautista, I was finally able to embed this geogebra worksheet! All the instructions for how to do this can be found at both their sites, which are both BRILLIANT!
I know I can probably get it to be a lot prettier, but for now here it is, and here's how you work it:
All you have to do is drag the point B around the circumference of the circle, and you will see something cool emerge, then drag the point D around, and another cool thing will emerge. You can also clean up between draggings with the reset button.