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 $A$. The ratio of the perimeter of the outer circle to that of polygon $ABCD$ is

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

Answer 1

Answer: (C)

$\frac{\pi }{2}$

Let the radius of the outer circle be r.
$\therefore$ perimeter of outer circle = $2\pi r$
But $OQ=BC=r$ [diagonals of the square BQCO]
$\therefore$ Perimeter of Square ABCD $=4r$
Hence, required ratio $=\frac{2\pi r}{4r}=\frac{\pi }{2}$