Question

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

Answer 1

Let radius of the circle be r and side of the square be a. As we can see, the diagonal of the square is equal to the diameter of the circle.

So, $\sqrt{2}a=2r$

$\Rightarrow a=\sqrt{2}r$

Now, ratio of area of the circle and the square $=\frac{\pi r^2}{a^2}=\frac{\pi r^2}{2r^2}=\pi :2$