Question

The distance between the centers of two circles is 6 cm. Radius of one circle is 1.7 cm and that of other circle is 2.8 cm. Draw a Indirect common tangent of these circle.

Answer 1

Given: r₁ = 17 cm, r₂ = 2.8 cm and the distance between these centers C₁₂ = 56 cm.

To Construct : indirect (transversal) common tangent.

Steps of Construction:

(1) Draw a line segment of the length of 6 cm the distance between two centers C₁C₂

(2) Taking C₁ as center and radius 1.7 cm draw a circle.

(3) Taking C₂ as center and radius 2.8 cm draw another circle.

(4) Draw the perpendicular bisector of C₁C₂ which intersects it at M.

(5) Taking M as center and radius MC₁ = MC₂ draw another circle.

(6) Taking the radius equal to the sum of two radii center C₁ the centre of smaller circle draw a circle.

i.e., radius 1.7 + 2.8 = 4.5 cm and center C₁ which intersects the circle with diameter C₁C₂ at A and B.

(7) Join AC₂ and AC₁ which intersect the circle radius 1.7 cm at P.

(8) Join P to Q.

Hence, PQ is the required indirect common tangent