Question

In a circle of diameter 40 cm the length of a cord is 20 cm. Find the length of minor arc corresponding to the cord.

Answer 1

Let arc $AB=S$. It is given that $OA=20$ cm and chord $AB=20$cm
Therefore, $\Delta OAB$ is an equilateral trianagles.Hence,
$\angle AOB$
$\angle AOB={60}^{\circ }={(60\times \frac{\pi }{180})}^c={\left(\frac{\pi }{3}\right)}^c$
Now,
$\theta =\frac{arc}{radius}\Rightarrow \frac{\pi }{3}=\frac{s}{20}\Rightarrow s=\frac{20\pi }{3}cm$