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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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