Question

A circle is inscribed in a square and the square is circumscribed by another circle. What is the ratio of the areas of the inner circle to the outer circle?

• A. $1:2$
• B. $1:\sqrt{2}$
• C. $\sqrt{2}:4$
• D. $1:\sqrt{3}$

Answer 1

The correct option is A $1:2$

Let side of square $=a$
$\therefore r=\frac{a}{2}.....\left(i\right)$
$\sqrt{2}a=2R$
$a=\sqrt{2}R.....\left(ii\right)$
$2r=\sqrt{2}R$
$\sqrt{2}R=R$
$\frac{\pi R^2}{\pi R^2}={\left(\frac{r}{R}\right)}^2=\frac{r^2}{2r^2}=\frac{1}{2}$.