Question:
Draw a circle of radius 3.5 cm. Draw a pair of tangents to this circle, which are inclined to each other at an angle of 60°. Write the steps of construction.
Solution:
Steps of Construction:
Step 1. Draw a circle with centre O and radius = 3.5 cm.
Step 2. Draw any diameter AOB of this circle.
Step 3. Construct $\angle B O C=60^{\circ}$, such that the radius $O C$ meets the circle at $C$.
Step 4. Draw $\mathrm{MA} \perp A B$ and $N C \perp O C$.
Let AM and CN intersect at P.
Then, PA and PC are the required tangents to the given circle that are inclined at an angle of 60o.