Question

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

Answer 1

Answer:

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Answer 2

Answer:

To construct: A pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°

Steps of Construction:

(a) Draw a circle of radius 5 cm and with centre as O.

(b) Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A with the help of compass.

(c) Draw a radius OB, making an angle of 120° (180° − 60°) with OA.

(d) Draw a perpendicular to OB at point B with the help of compass. Let both the perpendiculars intersect at point P. PA and PB are the required tangents at an angle of 60°.

Justification: The construction can be justified by proving that ∠APB = 60°

By our construction

∠OAP = 90°

∠OBP = 90°

And ∠AOB = 120°

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

∠OAP + ∠AOB + ∠OBP + ∠APB = 360°

90° + 120° + 90° + ∠APB = 360°

∠APB = 60°

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