Question

The distance between the centers of two circles with radii 3.2 cm and 1.5 cm respectively Is 6.2 cm. Draw the direct common tangents these circles. Measure these tangents and check your answer by calculation.

Answer 1

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