It might be a stretch, but after working it out i got r= sqrt(m^2 - (p-n)^2)/2

isnt the height = to the diamter, and if you made a right triangle, m would be the hypothenuse and p-n would be the short leg. so sqrt(m^2-(p-n)^2) would give you the height, divide by two, and you have your radius.

tell me if i am wrong...