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Question
Two circles touch each other externally. The sum of their areas is 58π cm2 and the distance between their centers is 10 cm. Find the radii of the two circles.
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Solution
Let r and R be the radius of the two circles.
r + R = 10 ....(1)
πr2 + πR2 = 58π .....(2)
Putting the value of r in (2)
r2 + R2 = 58
( 10 - R )2 + R2 = 58
100 - 20R + R2 + R2 = 58
2R2 - 20R + 42 = 0
R2 - 10R + 21 = 0
( R - 3 )( R - 7 ) = 0
R = 3, 7.
Hence the radius of the two circles is 3cm and 7cm respectively.
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