Question

In the given figure, $RST$ is the tangent to the circle with centre $O$, at $S.$ $AOS$ is a straight line $BO\parallel RT$ and $\angle ORS={46}^{\circ }.$ Then $\angle BAC$ equals

• A. ${22}^{\circ }$
• B. ${46}^{\circ }$
• C. ${23}^{\circ }$
• D. ${32}^{\circ }$

Answer 1

The correct option is C ${23}^{\circ }$

Given, $BO\parallel RT$
$\angle BOC=\angle ORS={46}^{\circ }$ ...(Alternate angles)
Thus, $\angle BAC=\frac{1}{2}\angle BOC=\frac{1}{2}\left(46\right)={23}^{\circ }$
Angle subtended by the chord at the circle is half the angle subtended by the chord at the centre.