Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of ${47}^{\circ }$, it is required to draw tangents at the end points of those two radii of the circle, the angle between the radii is

• A. ${123}^{\circ }$
• B. ${47}^{\circ }$
• C. ${133}^{\circ }$
• D. ${43}^{\circ }$

Answer 1

The correct option is C ${133}^{\circ }$

Angle subtended between the tangents PA and PB is ${47}^{\circ }$
$\therefore \angle APB={47}^{\circ }$


Now, PA and PB are tangents.
$\therefore OA\perp PAandOB\perp PB$
$\therefore$ In quadrilateral PAOB, by angle sum property of quadrilaterals,
$\angle APB+\angle PAO+\angle OBP+\angle AOB={360}^{\circ }$
$\Rightarrow {47}^{\circ }+{90}^{\circ }+{90}^{\circ }+\angle AOB={360}^{\circ }$
$\Rightarrow \angle AOB={133}^{\circ }$

Hence, the correct answer is option c.