Question

In the figure, if $\angle ABC={20}^0$ and $O$ is the centre, then $\angle AOC$ is equal to

• A. ${20}^0$
• B. ${40}^0$
• C. ${60}^0$
• D. ${10}^0$

Answer 1

Answer: (B)

${40}^0$

For the arc $AC,\angle ABC$ is subtended at the circumference while $\angle AOC$ is subtended at the centre of the circle.
SInce, angle subtended by the arc at the centre is twice that of the angle subtended at the circumference, $\angle AOC=2\angle ABC$
$\therefore \angle AOC={40}^0$

Hence, option B.