Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°

Construction Procedure:

The given circle tangents can be constructed in the following manner:

1. Draw a circle with O as the centre having radius as 5 cm.

2. On the circumference of the circle take a point Q and join OQ.

3. At point Q draw a perpendicular to QP.

4. Draw a radius OR with OQ, making a 120° angle i.e. (180°60°).

5. At point R draw a perpendicular to RP.

6. Now at point P both the perpendiculars intersect.

7. As a result, the required tangents are PQ and PR at an angle of 60°.

Justification:

By proving that ∠QPR = 60° the construction can be justified

By the above construction

∠OQP = 90°

∠ORP = 90°

And ∠QOR = 120°

As we know that the sum of all interior angles of a quadrilateral = 360°

∠OQP+∠QOR + ∠ORP +∠QPR = 360^o

90°+120°+90°+∠QPR = 360°

Hence, ∠QPR = 60°

As a result the above construction is justified