A, S, M and Dare functions of x and y, and they are defined as follows:

$A(x, y) + x + y$

$S(x, y) = x - y$

$M(x, y) = xy$

$D(x, y) = x/y$,

where $y \neq 0$.

The figure shows a rectangle ABCD with a semi-circle and circle inscribed inside it as shown. What is the ratio of the area of the circle to that the semi-circle?

- $(\sqrt{2}-1)^{2}$
- $2(\sqrt{2}-1)^{2}$
- $(\sqrt{2}-1)^{2}/2$
- None of these.