two circles touch internally, the sum of their areas is 116 pie sq cm and distances between their centres is 6cm. find the radii of the circles.
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let x,y radii
then πx^2+πy^2=116
so, x^2+y^2=58
also, x-y=6
so, (x-y)^2=36
so, x^2+y^2-2xy=36
so , 58-2xy=36
so, 22=2xy
so, xy=11
so, x=11/y
so, 11/y-y=6
so, y=1.5
x=7.5
then πx^2+πy^2=116
so, x^2+y^2=58
also, x-y=6
so, (x-y)^2=36
so, x^2+y^2-2xy=36
so , 58-2xy=36
so, 22=2xy
so, xy=11
so, x=11/y
so, 11/y-y=6
so, y=1.5
x=7.5
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