Two circles touch externally and sum of their areas is 130andpi; 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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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?

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CDS I - Mathematics Previous Year Question Paper 2016

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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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