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.

Step1: Draw a line PQ=8cm. taking P and Q as a center draw circle of 3cm and 4cm.

Step2: Now bisect PQ. We get midpoint of PQ be T.

Now take T as a center , draw a circle of PT radius , this will intersect the circle at point A,B,C,D. Join PB,PD,AQ,QC.

Justification:

It can be justified by prove that PB,PD are tangents of circle (whose center is P and radius is 3cm) and AQ,QC are tangents of circle (whose center is Q and radius is 4cm)

Join PA, PC, QB, QD

∠PBQ=90° (Angle is on semicircle)

BQ⊥PB

Since, BQ is radius of circle, PB has to be a tangent. Similarly PD, QA ,QC are tangents.