Question

Two circles touch each other externally. The sum of their areas is 74π cm² and the distance between their centers is 12 cm. Find the diameters of the circle.

Answer 1

Let the radius of the circles be r₁ and r₂.
So, r₁ + r₂ = 12 ⇒ r₂ = 12 - r₁

Sum of the areas of the circles = 74π
⇒ πr₁² + πr₁² = 74π
⇒ r₁² + r₁² = 74

⇒ r₁² + ( 12 - r₁ )² = 74
⇒ r₁² + 144 - 24r₁ + r₁² = 74
⇒ 2r₁² - 24r₁ + 70 = 0
⇒ r₁² - 12r₁ + 35 = 0
⇒ ( r₁ - 7 )( r₁ - 5 ) = 0
⇒ r₁ = 7  or      r₁  = 5
Ir r₁ = 7 cm, then r₂ = 5 cm
If r₁ = 5 cm, then r₂ = 7 cm
So, the diameters of the circles will 10 cm and 14 cm.