Steps of construction :
(1) First of all, we draw a line segment OO’ = 6.2 cm.
(2) Taking O as center and radius 3.2 cm, draw a circle.
(3) Taking O’ as center and radius 1.5 cm draw another circle.
(4) Taking OO’ as diameter, draw a circle.
(5) Taking center, the center of the larger circle and radius equal to the difference of the radii of two circle.
i.e., 3.2 – 15 = 17, draw another circle which intersects circle with diameter OO’ at A and B.
(6) Join OA and OB which intersects the larger circle when produced at A and B.
(7) From O’ the center of smaller circle draw O’Q || OP and O’Q || OP’.
(8) Join PQ, P’Q’, PQ and P’Q’are the required direct common tangents.
On measuring : we get.
PQ = P’Q’ = 6 cm
Calculation : PQ