Q24 of 31 Page 1

Draw a pair of tangents inclined to each other at an angle of 60o to a circle of radius 3 cm.

Steps of construction:


1. Draw a circle of radius 3 cm, with center O.



2. Draw OA and OB, such that A and B lie on the circumference of circle and ∠OAB = 120°



3. Draw AX ⊥ OA and BY ⊥ OB



4. AX and BY intersect each other at point P, PA and PB are required tangents.


To show: ∠APB = 60° [Angle between tangents]


In quadrilateral OAPB,


∠AOB + ∠OAP + ∠APB + ∠OBP = 360° [Angle sum property of quadrilateral]


Now,


∠AOB = 120° [By construction]


∠OAP = ∠OBP [Both 90°, By construction]


⇒ 120° + 90° + 90° + ∠APB = 360°


⇒ ∠APB = 60°


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