Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60∘ to each other.
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Draw a circle with radius 4 cm and construct two tangents to a circle such that when those two tangents intersect each other outside the circle they make an angle of 60° with each other
Analysis:
As shown in the figure,
In ▢AOBC,
∠A = ∠B = 90° ......[Tangent theorem]
∠C = 60° ......[Given]
∴ ∠O = 120° ......[Remaning angle of ▢AOBC]
Steps of constructions:
- With centre O, draw a circle of radius 4 cm.
- Take any point A on the circle and draw ray OA.
- Draw line l ⊥ ray OA at point A.
- Draw ray OB such that ∠AOB = 120°. Point B must be on the circle.
- Draw line m ⊥ ray OB at point B.
l and m are the required tangents.
Concept: To Construct Tangents to a Circle from a Point Outside the Circle.
Is there an error in this question or solution?
Steps of construction:
(i) Take a point O on the plane of the paper and draw a circle of radius OA = 4 cm.
(ii) Produce OA to B such that OA = AB = 4 cm.
(iii) Draw a circle with centre at A and radius AB.
(iv) Suppose it cuts the circle drawn in step (i) at P and Q.
(v) Join BP and BQ to get the desired tangents.
Justification:
In OAP, OA = OP = 4 cm ...(radii of the same circle)
Also, AP = 4 cm ….(Radius of the circle with centre A)
∴ ΔOAP is equilateral.
∴ ∠PAO = 60°
∴ ∠BAP = 120°
In BAP, we have BA = AP and ∠ BAP = 120°
∴ ∠ABP = ∠APB = 30°
Similarly we can get ∠ABQ = 30°
∴ ∠PBQ = 60°
Last updated at Jan. 18, 2022 by
This question is similar to Ex 11.2,4 - Chapter 11 Class 10 - Constructions
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Last updated at Jan. 18, 2022 by Teachoo
This question is similar to Ex 14.1, 3 Chapter 14 Class 10 - Statistics
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