Question

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

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

Answer 1

Answer: (C)

The correct option is C $\left(\frac{50\sqrt{2}}{\pi }cm\right)$

Given circumference of circle $=100cm$
Let radius of circle be $rcm$
Now, $2\pi r=100$
$r=\frac{100}{2\pi }=\frac{50}{\pi }$

Diagonal of square $=$ Diameter of circle $=2r$$=\frac{100}{\pi }cm$

Let the side of the square $=acm$

Now, diagonal of square $=\sqrt{a^2+a^2}$$=\sqrt{2}a$

$\Rightarrow \frac{100}{\pi }=\sqrt{2}a\Rightarrow a=\frac{100}{\sqrt{2}\pi }\Rightarrow a=\frac{100\sqrt{2}}{2\pi }\therefore a=\frac{50\sqrt{2}}{\pi }cm$