Draw a line segment AB of length 8 cm. Taking A as the 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

Solution:

Steps of construction:

1. Draw AB = 8 cm. With A and B as centres, radii as 4 cm and 3 cm respectively draw two circles.

2. Draw the perpendicular bisector of AB, intersecting AB at O.

3. With O as the centre and OA as radius draw a circle that intersects the two circles at P, Q, R and S.

4. Join BP, BQ, AR and AS.

5. BP, BQ are the tangents from B to the circle with centre A.

6. AR, AS are the tangents from A to the circle with centre B.

Proof:

∠APB = ∠AQB = 90° (Angle in a semi-circle)

∴ AP ⊥ PB and AQ ⊥ QB

Therefore, BP and BQ are the tangents to the circle with centre A.

Similarly, AR and AS are the tangents to the circle with centre B.

☛ Check: Class 10 Maths NCERT Solutions Chapter 11

Video Solution:

Draw a line segment AB of length 8 cm. Taking A as the 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

NCERT Solutions Class 10 Maths Chapter 11 Exercise 11.2 Question 5

Summary:

A line segment AB of length 8 cm. Taking A as the centre, a circle of radius 4 cm is drawn and taking B as centre, another circle of radius 3 cm is drawn. BP and BQ are the required tangents to the circle with centre A and radius 4 cm and AR and AS are the tangents to the circle with centre B and radius 3 cm.

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