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, 4 cm and 3 cm as radius 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.
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:
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
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.