Three circles are mutually tangent externally Their centers form a triangle whose sides are of lengths 3, 4, and 5. The total area of the circles (in square units) is-

Question: Three circles are mutually tangent externally Their centers form a triangle whose sides are of lengths 3, 4, and 5. The total area of the circles (in square units) is-

Solution:
let, the radiuses r₁, r₂, r₃ and let r₃>r₂>r₁

ATQ,
r₁ + r₂ = 3
r₁ + r₃ = 4
r₂ + r₃ = 5

r₃ = 5 - r₂

r₁ + 5 - r₂ = 4
⇒ r₂ = r₁ + 1

r₁ + r₁ + 1 = 3
⇒ 2r₁ = 2
∴ r₁ = 1

r₂ = 1 + 1 = 2
r₃ = 5 - 2 = 3

total areas = πr₁² + πr₂² + πr₃²
= π + 4π + 9π
= 14π