Draw a line connecting the centers of the circle. From each circle center draw a line to the edge of the square horizontally (or vertically, pick one).

So there are 2 horizontal lines equal to the radius of the circle and a 45 degree line connecting the centers of the circle with length twice the radius. The total horizontal distance covered by these lines is the edge of the square. From here, it should be easy to figure out the radius of the circle.