Question

In the given figure, if AOB is the diameter and MPQ is a tangent at P, then the value of $\angle MPA$ is

• A. ${25}^0$
• B. ${26}^0$
• C. ${27}^0$
• D. ${30}^0$

Answer 1

The correct option is D ${30}^0$


$\angle POB=2\times \angle BAP$
[Angle subtended at the centre by the segment is double of the angle subtended at the any other point on the circle by the same segment.]
$\angle BAP=\frac{{120}^0}{2}={60}^0$
In $OAP,\angle OPA=\angle OAP={60}^0$
[Equal angles opp to equal radius of the circle]
$\angle MPA=\angle OPM-\angle OPA(OP\perp MQ)$
$=90-60={30}^0$
Hence, d is the correct option.