Question

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

Answer 1

Given, Diameter$=40$

$\Rightarrow$Radius$\left(r\right)=20$

Length of chord$=20$

From above figure, we observe that the triangle $\Delta ABC$ is an equilateral triangle.

So, $\theta =60°\times \frac{\pi }{180}=\frac{\pi }{3}$ radians.

Since, angle in radian is $\theta =\frac{l}{r}$, where $l$ is arc length.
So, length of minor arc $l=r\theta$

$=20\times \frac{\pi }{6}$

$\therefore l=\frac{10\pi }{3}$