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Two circles touch externally and sum of their areas is 130π cm2 and the distance between their centres is 14 cm. What is the difference in the radii of the circles?
  • a)
    5 cm
  • b)
    6 cm
  • c)
    7 cm
  • d)
    8 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Two circles touch externally and sum of their areas is 130π cm2and ...

Suppose r and R are the radius of the circles
Sum of the areas of the circles = 130π cm2
⇒ π(R2 + r2) = 130π
⇒ (R2 + r2) = 130     ---- (1)
Distance between their centres = 14 cm
⇒ R + r = 14      ---- (2)
From equation 1 and 2
⇒ R2 + r2 = (R + r)2 – 2Rr
⇒ 130 = 196 – 2Rr
⇒ 2Rr = 66
⇒ Rr = 33      ---- (3)
From equation 2 and 3
⇒ R = 11 and r = 3
∴ Difference in the radii of the circles = 11 – 3= 8 cm
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Two circles touch externally and sum of their areas is 130π cm2and the distance between their centres is 14 cm. What is the difference in the radii of the circles?a)5 cmb)6 cmc)7 cmd)8 cmCorrect answer is option 'D'. Can you explain this answer?
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