Question

Two circles of radii 4 cm and 2.5 cm have their centres 5.5 cm apart. Draw direct common tangents to the circles.

Answer 1

Radius of first circle, R = 4 cm

Radius of second circle, r = 2.5 cm

Distance between their centers, d = 5.5 cm

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

1. Draw a line segment OO′ = 5.5 cm

2. With O and O′ as the centers and radii 4 cm and 2.5 cm, draw circles S₁ and S₂ respectively.

3. With O as the centre and radius = R – r = 4 – 2.5 = 1.5 cm, draw a circle S₃.

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

5. Join OX and produce it to meet circle S₁ at P.

6. Using set square, draw OP || O′Q.

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

NOTE: In a similar manner, another direct common tangent can be drawn to the two circles on the other side of the centers.