Q. 44.3( 279 Votes )

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

Answer :

Steps of construction:
1) Draw a circle of radius 5 cm, and draw a radius OA anywhere in the circle.

2) Taking OA as base, draw an angle AOB such that ∠AOB = 120°.

3) At A, Draw a line AX such that AX ⊥ OA.

4) At B, Draw a line BY such that BY ⊥ OB.

5) AX and BY intersect at P; AP and BP are required tangents.

1) Clearly, AP and BP are tangents since tangent at a point on the circle is perpendicular to the radius through point of contact.
2) In Quadrilateral OAPB, we have
∠OAP + ∠APB + ∠OBP + ∠AOB = 360°    [By Angle Sum Property]
⇒ ∠OAP + 90° + 90° + 120° = 360°
⇒ ∠OAP = 60°

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