In a circle of diameter 44 cm , the length of a chord is 22 cm . What is the length of minor arc of the chord?

• Correct answer
  A

  $\frac{484}{21} \mathrm{~cm}$
• B

  $\frac{242}{21} \mathrm{~cm}$
• C

  $\frac{121}{21} \mathrm{~cm}$
• D

  $\frac{44}{7} \mathrm{~cm}$

Solution

Given, diameter of circle $=44 \mathrm{~cm}$. $\begin{aligned} & \text { radius of circle }=22 \mathrm{~cm} \\ & \text {Chord of circle }=22 \mathrm{~cm}\end{aligned}$ In figure $\triangle \mathrm{OAB}$ is equilateral triangle. Angle is $60^{\circ}$. So, arc is $\frac{1}{6}$ times circumference. Length of arc $=\frac{1}{6} \times 2 \pi r=\frac{1}{6} \times 2 \times \frac{22}{7} \times 22$ $=\frac{484}{21} \mathrm{~cm}$

Hence, the correct answer is option: 'A'.