In the given figure, two concentric circles are shown with centre O. 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 quadrilateral ABCD?

A

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

B

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

C

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

D

$$\pi$$