Question

In the given figure, $PQ$ is tangent at a point $R$ of the circle with centre $O$, if $\angle TRQ={30}^{\circ }$, Find $m\angle PRS.$

• A. ${70}^o$
• B. ${60}^o$
• C. ${80}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${60}^o$

From figure, Given that

$\angle TRQ={30}^{\circ }$

$\angle TSR=\angle TRQ={30}^{\circ }$ (by Alternate segment therom).....(i)

$\angle TRS={90}^{\circ }$(Angle in semi circle)..............(ii)

From (i) & (ii) $\angle RTS={60}^{\circ }$ (Angle sum property in $△SRT$)

$\therefore \angle PRS=\angle RTS={60}^{\circ }$ (by Alternate segment therom)