Question

Draw two congruent circles of radii 3 cm, having their centres 8 cm apart. Draw a transverse common tangent.

Answer 1

Radius of first circle, R = 3 cm

Radius of second circle, r = 3 cm

Distance between their centers, d = 8 cm

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

1. Draw a line segment OO′ = 8 cm

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

3. With O as the centre and radius = R + r = 3 + 3 = 6 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.

NOTE: In a similar manner, another transverse common tangent can be drawn to the two circles.