It took me a while to figure out the construction of the particular tangent circle, but I finally got it and I saved it under two gsp graphs and one script. I played around with the tracing of the locus of points of the center of the tangent circle with animation, but every possible combination I tried did not work so I apparently do not understand how to trace a locus of points using animation, every time I tried I got the message that the path cannot move during an animation. I did look at the assignment to get a feel for what the locus would create and that was obviously an ellipse and it would seem reasonable that most locus traces of the centers of the different types of tangent circles would create some kind of elliptical figure. That is all I have other than a link to show you my construction: