The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.

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Solution

Let $r_{1}$ and $r_{2}$ be the radii of two circles $(r_{1} > r_{2})$ .

Given, $r_{1} + r_{2} = 7$ cm ...(1)

Difference of their circumferences = 8 cm (Given)

Adding (1) and (2), we get

$r subscript 1 plus r subscript 2 equals 7 fraction numerator r subscript 1 minus r subscript 2 equals begin display style 14 over 11 end style over denominator 2 r subscript 1 equals 7 plus begin display style 14 over 11 end style end fraction$

$2 r subscript 1 equals fraction numerator 77 plus 14 over denominator 11 end fraction equals 91 over 11 r subscript 1 equals 91 over 22 c m$

When, we get

$r subscript 2 equals 7 minus 91 over 22 r subscript 2 equals fraction numerator 154 minus 91 over denominator 22 end fraction equals 63 over 22 c m$

Circumference of one circle

Circumference of the other circle

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