Question

Construct a direct common tangent to two circles of radii 5 cm and 3 cm and whose centres are 2 cm apart

Answer 1

Radius of first circle, R = 5 cm

Radius of second circle, r = 3 cm

Here, R – r = 5 – 2 = 3 cm

Thus, the two circles touch each other internally.

Distance between their centers, d = 2 cm

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

1. Draw a line segment OO′ = 2 cm

2. With O and O′ as the centers and radii 5 cm and 3 cm, draw circles S₁ and S₂ respectively. Let these two circles touch each other at P.

3. Draw perpendicular XY to OO′ at P.

Thus, XY is the direct common tangent to the circles S₁ and S₂.