Question

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Answer 1

Here, diameter AB = 40 cm

Radius OA = 20 cm

Chord AC= 20 cm

$\therefore \Delta AOC$ is an equilateral triangle

So $\angle AOC={60}^0={\left(\frac{60\times \pi }{180}\right)}^C={\left(\frac{\pi }{3}\right)}^C$ $[\because radianmeasure=\frac{\pi }{180}\times degreemeasure]$

We know that ${\theta }^C=\frac{l}{r}$

$\therefore \frac{\pi }{3}=\frac{l}{20}\Rightarrow l=\frac{20\pi }{3}$ cm

Hence, length of minor arc of chord is $\frac{20\pi }{3}$

$ence,lengthofminorarcofchordis$\dfrac{20\pi}{3}$