Question

Draw two congruent circles of radii 4.5 cm whose centres are 9 cm apart. Draw transverse common tangents.

Answer 1

Radius of first circle, R = 4.5 cm

Radius of second circle, r = 4.5 cm

Distance between their centers, d = 9 cm

Here, R + r = 4.5 + 4.5 = 9 cm = d

Therefore, the two circles touch externally.

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

1. Draw a line segment OO′ = 9 cm

2. With O and O′ as the centers and radius 4.5 cm, draw circles S₁ and S₂ respectively. Let these two circles touch externally at point D.

3. Draw perpendicular PQ to OO^’ at point D

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