Question

Circles with centres A, B and C touch each other externally. If AB = 3 cm, BC = 3 cm, CA = 4 cm, then find the radii of each circle.

Answer 1

Let AP = AR = x, BP = BQ = y, CQ = CR = z .....[Radii of the same circle]

AP + BP = AB …[A – P – B]

∴ x + y = 3 …(i)

BQ + CQ = BC …[B – Q – C]

∴ y + z = 3 …(ii)

AR + CR = AC …[A – R – C]

∴ x + z = 4 …(iii)]

Adding equations (i), (ii) and (iii), we get

x + y + y + z + x + z = 3 + 3 + 4

∴ 2x + 2y + 2z = 10

∴ 2(x + y + z) = 10

∴ x + y + z = 5 …(iv)

Substituting equation (i) in equation (iv), we get 3 + z = 5

∴ z = 5 − 3

∴ z = 2 cm

Substituting equation (ii) in equation (iv), we get x + 3 = 5

∴ x = 5 − 3

∴ x = 2 cm

Substituting equation (iii) in equation (iv), we get

y + 4 = 5

∴ y = 5 − 4

∴ y = 1 cm

∴ The radii of circles with centres A, B, C are 2 cm, 1 cm and 2 cm respectively.