Question

Draw a pair of tangents to a circle of radius $5cm$ which are inclined to each other at an angle of ${60}^{\circ }$

Answer 1

Construction Procedure:
1. Draw a circle of radius $5cm$ and with centre as $O$.
2. Take a point $Q$ on the circumference of the circle and join OQ.
3. Draw a perpendicular to QP at point $Q$.
4. Draw a radius $OR$, making an angle of ${120}^{\circ }$ i.e. $({180}^{\circ }-{60}^{\circ })$ with OQ.
5. Draw a perpendicular to $RP$ at point $R$.
6. Now both the perpendiculars intersect at point $P$.
7. Therefore, PQ and $PR$ are the required tangents at an angle of ${60}^{\circ }$.