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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?

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? Correct Answer 8 cm

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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)

⇒ (14  -r)2 + r2 = 130

⇒ 196 + r2 - 28r + r2 = 130

⇒ 2r2 - 28r + 66 = 0

⇒ r2 - 14r + 33 = 0

⇒ r2 - 11r - 3r + 33 = 0

⇒ (r - 11)(r - 3) = 0

⇒ r = 11 & 3

⇒ R = 11 and r = 3

∴ Difference in the radii of the circles = 11 – 3= 8 cm

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