Construction 6: Draw a pair of direct common tangents to two circles of radii 2.6 cm and 1.7 cm respectively and the distance between whose centre is 5 cm.
Steps of Construction:
1. Draw a line segment OO' = 5 cm.
2. With O as centre and radius = 2.6 cm, draw a circle.
Taking O' as centre and radius = 1.7 cm, draw another circle.
3. Bisect OO' at M.
4. Taking M as centre and OM as radius draw a circle C(M, 1/2 OO').
5. Taking O as centre and radius = (2.6 - 1.7) cm = 0.9 cm, draw a
circle C(O, 0.9 cm) intersecting C(M, 1/2 OO') in A and B'.
6. Join OA and OB and produce then to meet the circle C(O, 2.6 cm) in P and a respectively.
7. Draw line segments O'R || OP and O'S || OQ to meet the circle C(O, 1.7 cm) at R and S respectively. Join PR and as. Thus, PR and as are required tangents.
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