Question

Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circle, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm.

Answer 1

AB = 6 cm, AC = 8 cm and BC = 9 cm

Let radii of the circles having centers A, B and C be r₁, r₂ and r₃ respectively.

r₁ + r₃ = 8

r₃ + r₂ = 9

r₂ + r₁ = 6

Adding

r₁ + r₃ + r₃ + r₂ + r₂ + r₁ = 8 + 9 + 6

2(r₁ + r₂ + r₃) = 23

r₁ + r₂ + r₃ = 11.5 cm

r₁ + 9 = 11.5  ...(Since r₂ + r₃ = 9)

r₁ = 2.5 cm

r₂ + 6 = 11.5  ...(Since r₁ + r₃ = 6)

r₂ = 5.5 cm

r₃ + 8 = 11.5  ...(Since r₂ + r₁ = 8)

r₃ = 3.5 cm

Hence, r₁ = 2.5 cm, r₂ = 5.5 cm and r₃ = 3.5 cm.