Question

If $\beta$ is the angle subtended at the center and $\alpha$ is the angle subtended at a point on the circumference of the circle, then $\alpha =$

• A. $\beta$
• B. $\frac{\beta }{2}$
• C. $2\beta$
• D. $3\beta$

Answer 1

The correct option is B $\frac{\beta }{2}$

Arc made an angle $\beta$ at the center $\text{O}$ of the circle.
The same arc made an angle $\alpha$ at a point in the remaining part of the circle.
So, the angle made by the arc at the center $\beta$ is $2$ times of the angle $\alpha$ made at the point in the remaining part of the circle.
$\Rightarrow \beta =2\times \alpha$
$\Rightarrow \alpha =\frac{\beta }{2}$