Question

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of ${60}^0$. Find the value of $\angle$ AOB.

• A. ${120}^{\circ }$
• B. ${40}^{\circ }$
• C. ${30}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is A

${120}^{\circ }$

Draw a circle of radius 5 cm. Mark its centre as O and mark a point A on the circle. Join OA.

Draw a line at A perpendicular to radius OA.

Draw OB at such that $\angle$ AOB is ${120}^{\circ }$ . [180 - 60 : Angle at centre and the angle between the two tangents are supplementary]

Draw a line at B perpendicular to radius OB. Let the perpendiculars at A and B meet at P.

PA and PB are the required tangents.

Here, $\angle APB={60}^{\circ }$