Question

In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If $\angle QPT=60°,$ find $\angle PRQ.$

• A. 90°
• B. 100°
• C. 110°
• D. 120°

Answer 1

The correct option is D 120°

Since, PT is a tangent to the circle,
$\angle OPT=90°...$ (tangent is perpendicular to the radius of a circle)
So,
$\angle OPT=\angle QPT+\angle OPQ\Rightarrow 90°=60°+\angle OPQ\Rightarrow \angle OPQ=30°$

Since,
$OP=OQ,\angle OPQ=\angle OQP=30°$

$\text{In}△OQP,\angle QPO+\angle OQP+\angle POQ=180°\Rightarrow 30°+30°+\angle POQ=180°\Rightarrow \angle POQ=120°$

So, $\angle POQ$ on the major arc $=360°-120°=240°$

So,
$\angle PRQ=\frac{1}{2}\text{central angle}$
$=\frac{1}{2}\times 240°$
$=120°$