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 = 360o
90°+120°+90°+∠QPR = 360°
Hence, ∠QPR = 60°
As a result the above construction is justified