Question

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

• A. $20\pi /3cm$
• B. $\pi /3cm$
• C. $19\pi /3cm$
• D. $2\pi /3cm$

Answer 1

Answer: (A)

Given, diameter $=40cm$
$\therefore$ Radius $\left(r\right)=\frac{40}{2}=20cm$
and length of chord, $AB=20cm$
Thus, $\Delta OAB$ is an equilateral triangle.
$\therefore \theta =60^{\circ }=60\times \frac{\pi }{180}$
$=\frac{\pi }{3}rad$
We know that, $\theta =\frac{\text{Arc AB}}{\text{radius}}$
$\Rightarrow ArcAB=\theta \times r=\frac{\pi }{3}\times 20$
$=\frac{20\pi }{3}cm$