maybe this comes too late, but nevertheless..
I only can offer you a more or less precise drawing with a result.
The thick black lines describe the situation of your problem. The thin blue lines are necessary to place Point R on the circle line. The red value is the result you are looking for.
Obviously the center of the blue circle is placed on the black circle too. Maybe this property is of some use for you.
PS.: I corrected my drawing because I measured the wrong angle.