Question

In the given figure if C is the centre of the circle and $\angle PQC={25}^0$ and $\angle PRC={15}^0$, then $\angle QCR$ is equal to

• A. ${40}^0$
• B. ${60}^0$
• C. ${80}^0$
• D. ${120}^0$

Answer 1

The correct option is C ${80}^0$


In $\Delta PCQ$
$\angle QPC=\angle PQC={25}^0$ [ Equal angles opp to equal radii of the circle]

Similarly,
$\angle CPR=\angle CRP={15}^0$

$\angle QPR=\angle QPC+\angle CPR=25+15={40}^0$
$\angle QCR=2\times \angle QPR=2\times 40={80}^0$ [ Angle subtended by the segment at the centre is double of the angle subtended by the same segment at any other point on the circle.]
Hence, c is the correct option.