Question

The radii of two circle are respectively 2.0 cm and 3.5 cm and the distance between their centers is 7 cm. Draw direct common tangents of two circles.

Answer 1

Steps of construction :

(1) Draw a line segment OO’ = 7 cm equal to distance between their centers.

(2) Taking O as center and radius 2.0 cm draw a circle.

(3) With O’ as center and radius of 3.5 cm draw another circle.

(4) With diameter OO’ draw another circle.

(5) With center ‘O’ the center of larger circle and with radius equal to difference of their radii i.e., r₁ – r₂ = 3.5 – 2.0 = 1.5 cm draw a circle, which intersects the circle OO’ at points A and B.

(6) Join O’A and O’B and produce to touch the larger circle at point Q and Q’.

(7) From point O the center of smaller circle draw O’Q || OP and O’Q’ || OP’

(8) Join Q and P’Q’. which are the required tangents.