Question

The circumference of a circle is $100cm$. Then the side of a square inscribed in the circle is :

• A. $\frac{100\sqrt{2}}{\pi }cm$
• B. $\frac{50\sqrt{2}}{\pi }cm$
• C. $\frac{100}{\pi }cm$
• D. $50\sqrt{2}cm$

Answer 1

The correct option is B $\frac{50\sqrt{2}}{\pi }cm$

Since a square is inscribed inside a circle, the diagonal of the square will be a diameter of the circle.
Therefore,
$\sqrt{2}\times a=2r$
But, $C=2\pi r$
$\Rightarrow \sqrt{2}\times a=2\times \frac{C}{2\pi }$
$a=\frac{100}{\sqrt{2}\times \pi }$
$\therefore a=\frac{50\sqrt{2}}{\pi }$