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Question
Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.
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°
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