Two circles touch internally. The sum of their areas is 73 π sq.cm. and the distance between their centres is 5 cm. Find the radii of the circles.
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Two circles touch internally. The sum of their areas is 73 π sq.cm. and the distance between their centres is 5 cm. Find the radii of the circles.
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Answer:
8 cm and 3 cm
Step-by-step explanation:
let the radius be r1 and r2
then r1^2 + r2^2 = 73
r1-r2= 5
or (r1-r2)^2 = 25
or r1^2 +r2^2 - 2r1r2 =25
or 2r1r2 = 73-25 = 48
or r1r2= 24
(r1+r2)^2 = r1^2+r2^2+2r1r2 = 73+48= 121
hence r1+r2= 11
r1-r2= 5
hence 2r1 = 11+5=16
hence r1=8
hence r2= 3