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Two circles touch externally. The sum of their areas is 130p sq. cm. and the distance between their centres is 14 cm. The radius of the bigger circle is (Take π = 22/7)
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- 22 cm.
- 11 cm.
- 33 cm.
- 44 cm.
- 22 cm.
Correct Option: B
Let OA = R and O’A = r cm.
According to the question,
πR² + πr² = 130π
⇒ R² + r² = 130 ..... (i)
Again, R + r = 14 cm.
⇒ r = (14 – R) cm.
∴ R² + r² = 130
⇒ R² + (14 – R)² = 130
⇒ R² + 196 – 28R + R² = 130
⇒ 2R² – 28R + 196 – 130 = 0
⇒ 2R² – 28R + 66 = 0
⇒ R² – 14R + 33 = 0
⇒ R² – 11R – 3R + 33 = 0
⇒ R (R – 11) – 3 (R – 11) = 0
⇒ (R – 11) (R – 3) = 0
⇒ R = 11 or 3 cm.
∴ r = 3 or 11 cm.
∴ Radius of larger circle
= 11 cm.
