Question

If a square is inscribed in a circle, then the ratio of the areas of the circle and the square is

• A. $\pi :2$
• B. $2:\pi$
• C. $\pi r:2$
• D. $2:\pi r$

Answer 1

The correct option is A $\pi :2$

Let side of square $=a$
Radius of circle $=r$.
From $\Delta OEB$
$\Delta OEB$ is right angled triangle
Applying pythagoroes theorem
$O{E}^2+E{B}^2=O{B}^2$
${\left(\begin{array}{c}\frac{a}{2}\end{array}\right)}^2+{\left(\begin{array}{c}\frac{a}{2}\end{array}\right)}^2=r^2$
$2\frac{a^2}{4}=r^2$
$a^2=2r^2$
$a=\sqrt{2}r$.
$\frac{Areaofcircle}{Areaofsquare}=\frac{\pi r^2}{a^2}$
$=\frac{\pi r^2}{2r^2}$
$=\pi :2$.