Question

The length of the minor arc ACB of a circle $⨀$(0, r) is 1/6 part of its circumference. Then the measure of angle of minor arc ACB subtending at the centre is ................

• A. 60
• B. 90
• C. 30
• D. 120

Answer 1

Answer: (A)

60

Suppose, an arc $ACB$ subtends an angle $\theta$ at the centre of the circle $(0,r)$

Here it is given that,
Length of the minor arc $ACB=\frac{1}{6}\times$ circumference

We know that, Length of an arc with angle $\theta =\frac{\pi r\theta }{180}$
$⟹\frac{\pi r\theta }{180}=\frac{1}{6}\times 2\pi r$
$\therefore \theta =\frac{2\times 180}{6}=60$

Hence, the answer is ${60}^o$