Question

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

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

Answer 1

Answer: (A)

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