Question

Draw two direct common tangents to two circles of radii 5.5 cm and 3.5 cm and their centres are 9 cm apart

Answer 1

Radius of first circle, R = 5.5 cm

Radius of second circle, r = 3.5 cm

Distance between their centers, d = 9 cm

Since R + r = 5.5 + 3.5 = 9 cm, the two circles touch each other externally.

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

1. Draw a line segment OO′ = 9 cm

2. With O and O′ as the centers and radii 5.5 cm and 3.5 cm, draw circles S₁ and S₂ respectively.

3. Draw perpendiculars at O and O′ that intersect the circle with centre O at A and B, and the circle with centre O′ at M and N.

4. Join AM and BN.

Thus, AM and BN are the two direct common tangents.