Question

A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the major arc.

• A. ${150}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B

${30}^{\circ }$

Given that AO = AB=OB.

Since all sides are equal, $△AOB$ is equilateral, and hence equiangular. Also, each angle of the triangle equals ${60}^{\circ }.$
i.e.,$\angle$AOB = ${60}^{\circ }$

$⟹\angle ACB=\frac{1}{2}AOB$
($\because$ Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. )

$⟹\angle ACB=\frac{{60}^{\circ }}{2}={30}^{\circ }$