Geometry challenge

Nothing to do with Mathcad, but I know some of you enjoy a good challenge.  And I'm stumped.  Here's the situation:  Two circles of different diameters, one vertically offset a distance e from the other.  Vanes of thickness t are centered in the smaller circle.  The vane are 90 degrees from each other.  What are the top and bottom colored areas?  I'll gladly take any hints on how you'd do it.

Thanks!