Inspired by a gif from math-ani.
http://mathani.tumblr.com/post/87697580095/based-on-the-wonderful-johnsons-theorem
Johnson's Theorem is about the circumcircle for the triangle formed by the non-common intersection points. I thought the rhombi were a neat way of showing it.
Thinking about how to animate the circles to show it was interesting, too. I made a constant ratio between slow, medium and fast (so fast is ratio^2*slow), which made for interesting cycloid-like patterns for the intersection points.
Lots of relationships to notice, so hope you have some fun.