Question

If the side of a square is $24$ cm, then the circumference of its circumscribed circle is

• A. $24\sqrt{3}\pi$
• B. $24\sqrt{2}\pi$
• C. $12\sqrt{2}\pi$
• D. $24\pi$

Answer 1

The correct option is B $24\sqrt{2}\pi$

Diagonal $BD$ of the square

subtends right

angle (90${}^0$ ) at $C$, hence

$BD$must be the diameter of circumcircle

$\Rightarrow$ $BD$ = $2x$ (radius of circle)

$\Rightarrow$ 2r = $BD$ = $\sqrt{{BC}^2+{CD}^2}$

$\Rightarrow$ 2r= $24\sqrt{2}$

$\Rightarrow$$r$ =$\frac{24}{\sqrt{2.}}$

Circumference = 2$\pi \times r$= $\frac{2\pi \times 24}{\sqrt{2}}$

= $24\sqrt{2}\pi$.

$\therefore$ option $B$ Answer.