lol my method is logic based.
To find the centre of a square, you draw a straight line from both
corners, the point where they intersect is the middle of the
square.
since they said the square is perfectly centred on the circle, it
would be safe to say that the centre of the square is also the
exact centre of the circle.
Take the distance, from the two poles( BLue Line ) and voila,
radius 
