Three circles touch each other externally when the distance between their centres are 4 cm and 5 cm and 6 cm. Find the total radius of three circles.

Three circles touch each other externally when the distance between their centres are 4 cm and 5 cm and 6 cm. Find the total radius of three circles. Correct Answer 7.5

Given:

Three circles touch each other externally when the distance between their centres are 4 cm

and 5 cm and 6 cm.

Calculation:

Let O, P, Q be the centres of the three circles and they touch each other at M, N and S points.

OP = 4 cm, PQ = 5 cm, QO = 6 cm

Let OM = OS = r

⇒ MP = PN = 4 – r

⇒ SQ = NQ = QO – OS = 6 – r

⇒ NQ + PN = PQ = 5

⇒ 6 – r + 4 – r = 5

⇒ 2r = 5

⇒ r = 5/2

⇒ OM = 5/2

⇒ MP = 4 – 5/2 = 3/2

⇒ NQ = 6 – 5/2 = 7/2

⇒ OM + MP + NQ = 15/2 = 7.5

∴ Total radius of three circles is 7.5 cm.