The point of tangency is the center of the rectangle = ( 50,25)
The center of the circle on the top left = (r, 50) where r is the radius
So the distance from ( r, 50) to (0 ,50) = the distance from (r , 50) to (50,25)
Using the square of the distance formula we have that
r^2 = (r -50)^2 + ( 50 -25)^2
r^2 = r^2 - 100a + 2500 + 625
100r = 3125
r = 31. 25 = the radius