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InterviewSolution
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Two circles touch each other externally. The sum of their area is `490pi cm^(2)`. Their centres are separated by 28 cm. Find the difference of their radii (in cm).A. 14B. 7C. 10.5D. 3.5 |
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Answer» Correct Answer - A Let the radii of the circles be denoted by `r_(1)` cm and `r_(2)` cm where `r_(1) ge r_(2)`. As the circles touch each other externally, distance between their centres = Sum of their radii. ` :. R_(1)+r_(2)=28 " (1)" ` Also `pi(r_(1))^(2)+pi(r_(2))^(2)=490 pi` ` :. (r_(1))^(2)+(r_(2))^(2)=490 " (2)" ` Squaring both sides of Eq. (1), we get `(r_(1))^(2)+(r_(2))^(2) + 2(r_(1))(r_(2))=784` `r_(1)*r_(2)=147 " (3)" ` Solving Eqs. (1) and (3), we get `r_(1)=21 and r_(2) =7. ( :. r_(1) ge r_(2))` ` :. ` Required difference = 14 cm. |
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