Question

The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.

Answer 1

Let AB be the chord and O be the centre of the circle.
Here,
AO = BO = AB = 30 cm
Therefore,
∆ AOB is an equilateral triangle .
Now,
Radius = 30 cm
\[\theta = 60^\circ = \left( 60 \times \frac{\pi}{180} \right) = \frac{\pi}{3}\text{ radian }\]

\[\theta = \frac{\text{Arc}}{\text{Radius}}\]
\[ \Rightarrow \frac{\pi}{3} = \frac{\text{Arc}}{30}\]
\[ \Rightarrow \text{Arc} = \frac{30\pi}{3} = 10\pi cm\]