Question

Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.

Answer 1

Let the two circles having centres P and R touch each other externally at point Q.

Here, PQ = 5.5 cm, QR = 4.2 cm

The two circles touch each other externally.        ...(P−Q−R)

If the circles touch each other externally, distance between their centres is equal to the sum of their radii.

∴ By theorem of touching circles,

∴ PR = PQ + QR      

∴ PR = 5.5 + 4.2

∴ PR = 9.7 cm

∴ The distance between the centres of the circles is 9.7 cm.