Question 37284
If its diagonals are 12 and 24, and they meet at right angles, the side of the rhombus is the Pythagorean sum of 6 and 12, which is sqrt(180) or 6*sqrt(5).  Since the circle fits as tightly as possible within the rhombus, I'm thinking its diameter is the same.  Hence the radius is 3*sqrt(5).