Question

If the length of a minor arc $\widehat{AB}$ of a circle is $\frac{1}{4}$ of its circuference, then the angle subtended by the minor arc $\widehat{AB}$ at the center will be

• A. $30$
• B. $45$
• C. $90$
• D. $60$

Answer 1

The correct option is C $90$

Length of the minor arc $AB=\frac{\pi r\theta }{180}$, where $\theta$ is the angle subtended by $AB$ at the centre
$\therefore \frac{1}{4}\times \text{circumference}=\frac{\pi r\theta }{180}$
$\therefore \frac{1}{4}\times 2\pi r=\frac{\pi r\theta }{180}$
$\therefore \frac{1}{4}\times 2\pi r\times \frac{180}{\pi r}=\theta$
$\therefore \theta ={90}^o$