I'm not so sure, I just drew this a diagram in A9CAD (poor man's autoCAD).
I know the diagrams a bit convoluted, but it seems to show that the path of the tip of the bit is the same as the path of the centre, but 'r' units lower in the Y-axis, and that the path of the centre is the same as the circumference of your desired radius fretboard radius + the radius of the cutting bit... hence the equation.
Obviously you are only cutting a small section of the top of that circle for your fretboard radius, but I drew the whole circle to try to illustrate the point.
I can email you the original above diagram in DWG format if you like.
I should probably do my own maths work now, I hope I helped you somehow.
Ben
EDIT, I had to shrink the image because it was too big (640x640), am I right in thinking 640x480 is the allowed limit?