Draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60^o 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 ΔOAP, 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^o
∴ ∠BAP = 120^o
In ΔBAP, we have BA = AP and ∠ BAP = 120^o
∴∠ABP = ∠APB = 30^o
Similarly we can get ∠ABQ = 30^o
∴ ∠PBQ = 60^o

Some More Questions From Areas Related to Circles Chapter

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Areas Related To Circles

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

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

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

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 5.

Mock Test Series

NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Areas Related To Circles

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

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

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

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle.

Draw a line segment of length 7.6 cm and divide it in the ratio 3 : 5.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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