Question

In the given figure with B as centre, the length of the minor arc AC subtending an angle $\theta$ at the centre is y and the circumference is x. Find the ratio y : x.

• A. x = (y × θ)/360
• B. x = (y × θ)/180
• C. y = (x × θ)/360
• D. y = (x × θ)/260

Answer 1

The correct option is A

x = (y × θ)/360

Length of the arc is directly proportional to the angle subtended at the centre.
Given, that an angle $\theta$ is subtended by an arc of length y.
For the full circle, the angle is ${360}^{\circ }$ and the arc length is the circumference, x.

$\frac{y}{\theta }=\frac{x}{360}$
$\Rightarrow \frac{y}{x}=\frac{\theta }{360}$