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:

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

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

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

Join BP, BQ, AR and AS.

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

AR, AS are the tangents from A to the circle with centre B.
Proof:
∠APB = ∠AQB = 90° (Angle in a semicircle)
∴ 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.
☛ Related Questions:
 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.
 Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
 Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 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 is inclined to each other at an angle of 60°.
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