Question

Construct a transverse common tangent to two circles of radii 2.5 cm and 3 cm with their centres 10 cm apart.

Answer 1

Radius of first circle, R = 2.5 cm

Radius of second circle, r = 3 cm

Distance between their centers, d = 10 cm

The steps below need to be followed to construct a transverse common tangent to the two circles.

1. Draw a line segment OO′ = 10 cm

2. With O and O′ as the centers and radii 2.5 cm and 3 cm, draw circles S₁ and S₂ respectively.

3. With O as the centre and radius = R + r = 2.5 + 3 = 5.5 cm, draw a circle S₃.

4. From the external point O′, draw a tangent O′X to circle S₃.

5. Join OX such that it cuts circle S₁ at P.

6. Using set square, draw O′Q || OP.

Thus, PQ is a transverse common tangent to the circles S₁ and S₂.