Cirference of an Inscribed Circle?

Not too hard... we know the diagonal of the square is 8 root 2. This is the hypotenuse of an isosceles right-angled triangle, with angles of 45 degrees. This has sides in the proportion 1:1:root 2, so each side of the square must be 8 metres. So, the diameter of the circle is 8 metres. So, the cirference is 8pi.