Question

The circumference of a circle is 100 cm 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 $\frac{50\sqrt{2}}{\pi }cm$

The circumference of circle = 100 =$2\pi r$

Then $r=\frac{50}{\pi }$

Then $(diagonal{)}^2=2(side{)}^2$

So diagonal=$\sqrt{2}side=2\left(a\right)$

$\frac{50}{\pi }=\sqrt{2}side\left(a\right)$

Then side $a=\frac{50}{\pi \sqrt{2}}$ cm