Request for help with 2 triangles problem

I have been trying to solve a problem; originally I was thinking of it as 2 circles, but it is basically a problem of triangles, please see the attached file:http://www.roughmustard.com/problem.bmpI know the distance between A and B, the length of r and the angle a. When I draw it out there can only be 1 answer per set of variables, but I can't get a handle on how to calculate any of the other lengths of the triangles' sides.

If anyone can point me in the right direction I would be greatful.