Two circles touch each other externally. The sum of their

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Two circles touch each other externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is

1. 2 cm
2. 4 cm
3. 5 cm
4. 3 cm

Correct Option: D

Using Rule 14,

OO' = r₁ + r₂ = 14 cm. --(i)
Again, πr₁² + πr₂² = 130π
⇒ r₁² + r₂² = 130
⇒ r₁² + (14 – r₁)² = 130
[From equation (i)]
⇒ r₁² + 196 – 28r₁ + r₁²= 130
⇒ 2r₁² – 28r₁ + 196 – 130 = 0
⇒ 2r₁² – 28r₁ + 66 = 0
⇒ r₁² – 14r₁ + 33 = 0
⇒ r₁² – 11r₁ – 3r₁ + 33 = 0
⇒ r₁ (r₁ –11) – 3 (r₁ –11) = 0
⇒ (r₁ –11) (r₁ – 3) = 0
⇒ r₁ = 11 or] 3 cm.
∴ r₂ = 3 or] 11 cm.