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Two circles touch 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:
Answer & Solution
Correct Answer:
Option
B
Let smallest circle radius = R
Then biggest circle radius = (14 - R)
According to the question,
⇒ π(14 - R)22 + πR2 = 130π
⇒ (14 - R)2 + R2 = 130
⇒ 196 + R2 - 28R + R2 = 130
⇒ R = 3 cm
⇒ Radius of smallest circle
R = 3 cm
Then biggest circle radius = (14 - R)
According to the question,
⇒ π(14 - R)22 + πR2 = 130π
⇒ (14 - R)2 + R2 = 130
⇒ 196 + R2 - 28R + R2 = 130
⇒ R = 3 cm
⇒ Radius of smallest circle
R = 3 cm
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