Question

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

• A. $\frac{\pi }{3}$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

The correct option is C $\frac{\pi }{2}$

Let the diagonal of PQRS be 2r.
Therefore, side $=r\sqrt{2}.$
Now, ABCD is a square. And side $\frac{r\sqrt{2}}{2}\times \sqrt{2}=r.$
Perimeter of ABCD = 4r.
Circumference of bigger circle = 2 $\pi$r.
Therefore, required ratio $\frac{\pi }{2}$