It may happen that one has a collection of disks (with radius rd) at hand and wishes to know the radius of the circle, rc, around which to place them to make the division plate.

N = number of divisions desired
S = sin (180/N)

Then the equation for the disk radius when rc is given, as derived in the diagram is:

rd = rc * S / (1 - S)

so, to find rc when the disk radius, rd, is given, we simply invert this equation:

rc = rd * (1 - S) / S