draw a pair of tangent to a circle of radius 5 cm which are inclined to each other at an angle of 60
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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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