Solution:

To draw the circle and the two tangents we need to see how we proceed. We only have the radius of the circle and the angle between the tangents. We do not know the distance of the point from where the tangents are drawn to the circle and we do not know the length of the tangents either. We know only the angle between the tangents. Using this, we need to find out the distance of the point outside the circle from which we have to draw the tangents.

To begin, let us consider a circle with centre ‘O’ and radius 5cm. Let PA and PB are two tangents draw from a point ‘P’ outside the circle and the angle between them is 60°. In this ∠APB = 60°. Join OP.

Also we know,

OP is the bisector of ∠APB

Now In △ OAP,

OP = cm

Now we can a circle of radius 5cm with center 'O' we then mark a point at a distance of 10 cm from the center of the circle.Join OP and complete the construction as given in construction.Hence PA and PB are the required pair of tangents to the given circle

You can also try this construction without using trigonometric ratio

In △OAP ; ∠A=90° , ∠P=30° , ∠O=° and OA = cm. Construct △ AOP to get P