Question

Two circles of radii 5 cm and 3 cm have their centres 10 cm apart. Draw a direct common tangent to the circle.

Answer 1

Radius of first circle, R = 5 cm

Radius of second circle, r = 3 cm

Distance between their centers, d = 10 cm

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

1. Draw a line segment OO′ = 10 cm

2. With O and O′ as the centers and radii 5 cm and 3 cm, draw circles S₁ and S₂ respectively.

3. With O as the centre and radius = R – r = 5 – 2 = 3 cm, draw circle S₃.

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

5. Join OX and produce it to cut 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.