Question

If the length of a chord of a circle is equal to its radius, then the angle subtended by it at the minor arc of the circle will be,

• A. ${60}^{\circ }$
• B. ${75}^{\circ }$
• C. ${120}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is D ${150}^{\circ }$

Let $AB$ be the chord, then the angle subtended by $AB$ at the minor arc of the circle is $\angle ACB.$
Given, $OA=OB=AB$
$\Rightarrow$ $△OAB$ is equilateral
$\Rightarrow$ $\angle AOB={60}^{\circ }$
$\Rightarrow$ Reflex $\angle AOB={360}^{\circ }-{60}^{\circ }={300}^{\circ }$
$\therefore$ $\angle ACB=\frac{1}{2}\times$Reflex $\angle AOB=\frac{1}{2}\times {300}^{\circ }={150}^{\circ }$

(Angle at the centre$=2\times$angle at any pt. on remaining part of the circle)