Question

The area of the largest square that can be inscribed in a circle of radius $r$ units is

• A. $r^2\text{sq.units}$
• B. $2r^2\text{sq.units}$
• C. $3r^2\text{sq.units}$
• D. $4r^2\text{sq.units}$

Answer 1

The correct option is B $2r^2\text{sq.units}$


The largest square that can be inscribed in a circle must have diagonal of square equal to the diameter of that circle.
Let the side of square be $a$ units.
$\Rightarrow$ Length of diagonal of square $=a\sqrt{2}\text{units}$
$\Rightarrow a\sqrt{2}=2r$
$\Rightarrow a=\frac{2r}{\sqrt{2}}$
$\Rightarrow a=\sqrt{2}r$
Area of square $=a^2$
$=(\sqrt{2}r{)}^2$
$=2r^2\text{sq.units}$
Hence, the correct answer is option b.