Draw a line segment PQ of length 9cm. With P and Q as centres, draw circles of radius 5cm and 3cm respectively. Construct tangents to each circle from the centre of the other circle.
Step1: Draw a line PQ = 9 cm. taking P and Q as centres draw
circles of radii 5 cm and 3 cm.
Step2: Now bisect PQ. We get midpoint to be T.
Now take T as a center , draw a circle of PT radius , this will intersect
the circle at points A, B, C, D. Join PB, PD, AQ, QC.
Justification:
It can be justified by proof that PB, PD are tangents of circle (whose centre is P and radius is 5 cm) and AQ, QC are tangents of circle (whose centre is Q and radius is 3 cm)
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.