Two circles touch externally. The sum of their areas is 58 π cm^{2} and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm)
Ans: Sum of areas = Π r^{2} + Π (10 - r )^{2} = 58 Π Π r^{2} + Π (100 - 20 r + r^{2}) = 58 Π
r^{2} + 100 - 20r + r^{2} = 58
2r^{2} - 20r +100 - 58 = 0
2r^{2} - 20r +42 = 0 r^{2} - 10r +21 = 0
(r-7), (r-3) = 0
r=7cm,3cm