Question

Given a circle with O as the centre. Find the value of x.

• A. 80°
• B. 150°
• C. 50°
• D. 40°

Answer 1

Answer: (A), (D)

The correct options are
A

80°

D

40°

$\Delta AOB$ is an isosceles triangle (OA = OB; Radii),

$\Rightarrow \angle OAB=\angle OBA={50}^{\circ }.$

$\text{In}\Delta AOB,$

$\angle OAB+\angle OBA+\angle AOB={180}^{\circ }$

$\text{Hence,}\angle AOB={80}^{\circ }$

The angle subtended by an arc of the circle at its centre is double the angle subtended by it at any point on the remaining part of the circle.
Therefore, $\angle ACB=\frac{1}{2}\angle AOB={40}^{\circ }$.