Question

In the adjoining figure, 'O' is the centre of the circle and PQ , PR and ST are the three tangents. $\angle QPR={50}^{\circ }$, then the value of $\angle SOT$ is

• A. can't be determined
• B. ${65}^{\circ }$
• C. ${30}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${65}^{\circ }$

$\angle ROQ$ = 180 - 50 = ${130}^{\circ }$
$(\because \angle OQR+\angle ORP+\angle QOR+\angle QPR={360}^{\circ }and\angle OQP=\angle ORP={90}^{\circ })$
Now, Since RT = TM and QS = SM
$\therefore$ also OR = OM = OQ
$\therefore \angle ROT=\angle TOMand\angle MOS=\angle SOQ\therefore \angle SOT=\frac{1}{2}\angle ROQ\therefore \angle SOT=\frac{130}{2}={65}^{\circ }$