Question

In the given figure, AE and BC are chords of the circle, O is the centre of the circle and $\angle AOB={60}^{\circ }.$ The value of $(\angle AEB+\angle ACB)$ is

• A.
  ${60}^{\circ }$
• B.
  ${120}^{\circ }$
• C.
  ${150}^{\circ }$
• D.
  ${90}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$
We know that the 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.

$\therefore \angle AOB=2\angle AEB\Rightarrow {60}^{\circ }=2\angle AEB\Rightarrow \angle AEB={30}^{\circ }\dots ..\left(i\right)\text{Similarly,}\angle AOB=2\angle ACB\Rightarrow {60}^{\circ }=2\angle ACB\Rightarrow \angle ACB={30}^{\circ }\dots ..\left(ii\right)\text{Adding (i) and (ii), we get}\angle AEB+\angle ACB={30}^{\circ }+{30}^{\circ }={60}^{\circ }$

Hence, the correct answer is option (a).