Question

In the diagram, a square is drawn such that the diagonally opposite corners touch the Centre and the circumference of a circle whose radius is r. Find the area of the square.

• A. $\frac{r^2}{4}$
• B. $2r^2$
• C. $r^2$
• D. $\frac{r^2}{2}$

Answer 1

The correct option is D

$\frac{r^2}{2}$

The two diagonally opposite corners of the square are touching the centre and the circumference of the circle. We can conclude that the length of the diagonal is equal to the radius of the circle, which is r.

The measure of the diagonal of a square
$=\sqrt{2}\times \text{side of the square}$

Hence,
Radius of the circle,
$r=\sqrt{2}\times \text{side of the square}$

Side of the square
$=\frac{r}{\sqrt{2}}$

Area of the square
$=sid{e}^2=\frac{r}{\sqrt{2}}\times \frac{r}{\sqrt{2}}=\frac{r^2}{2}$