Sum of their areas is given find radii of the two circles, Mathematics

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Two circles touch externally. The sum of their areas is 58 π cm² and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm)

Ans: Sum of areas = Π r² + Π (10 - r )² = 58 Π Π r² + Π (100 - 20 r + r²) = 58 Π

r² + 100 - 20r + r² = 58

2r² - 20r +100 - 58 = 0

2r² - 20r +42 = 0 r² - 10r +21 = 0

(r-7), (r-3) = 0

r=7cm,3cm

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