Hey guys! Just stopping by and sharing how the third circle came to be:
http://img96.imageshack.us/img96/1656/rosewindowscreenshot1.png
You can probably trace what I did here... I was following Jean Lemire's guide (thank you very much for that, by the way!) and found a pretty simple method. I drew the tangent of the first circle you suggested I use and then drew a line from the radius of the second circle off to the right along the red axis. I found the radius of the third circle was exactly one-half the radius of the second, so I made a line of that distance and aligned it to the green axis at the point where the tangent and the radius-line-thingy met. The other end of that line was the center of the circle, and from there I drew the shape. π
That may be unclear, and if so, I apologize... I didn't bother to label the lines or anything. The only thing that bothers me is that the first and third circles don't exactly meet up, but it's understandable considering they're all using under 40 sides. It's not very noticeable from afar anyway.