Question

The largest possible square is inscribed in a circle having circumference $2\pi$ units. The area of the square in the square units is

• A. $4\pi \sqrt{2}$ sq. units
• B. $2\pi \sqrt{2}$ sq. units
• C. $\sqrt{2}$ sq. units
• D. $2$ sq. units

Answer 1

The correct option is D $2$ sq. units

Circumference $=$ $2\pi r=2\pi$ (Given)
$\Rightarrow$ $r=1$ unit
$\therefore$ Diagonal of square $=2$ units
Let each side of the square $=a$ units. Then
$a^2+a^2=4\Rightarrow 2a^2=4\Rightarrow a=\sqrt{2}$
$\Rightarrow$ Area of square $=$ $\left(\sqrt{2}\right)\left(\sqrt{2}\right)=2$ sq units