The figure below shows two concentric circles with centre 0. PQRS is a square, inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?

A

$$\frac{\pi}{4}$$

B

$$\frac{3\pi}{2}$$

C

$$\frac{\pi}{2}$$

D

$$\pi$$