hard geometry

Call the center of the circle $L$

$SL=r$

$KL=r$

$OL=45-r$

By pythagorean theorem:

(Hypotenuse of Triangle SOK)^2 - (Longer side of triangle SOK)^2= (Hypotenuse of triangle KOL)^2 - (Shorter side of triangle KOL)^2

$52^2-45^2=r^2-(45-r)^2$

Now it's your turn to solve.