Question 869347
two circles have circumferences that add up to 12(pie) centimeters, and areas that add up to 20(pie) square centimeters. Find the radius of each circle.
let x=radius of larger 1st circle
let y=radius of smaller 2nd circle
circumference of 1st circle=2πx
circumference of 1st circle=2πy
2πx+2πy=12π
x+y=6
y=6-x
..
area of 1st circle=πx^2
area of 2nd circle=πy^2=π(x-6)^2
πx^2+πy^2=20π
x^2+y^2=20
x^2+(6-x)^2=20
x^2+36-12x+x^2=20
2x^2-12x+16=0
x^2-6x+8=0
(x-4)(x-2)=0
x=4
or
x=2
radius of larger 1st circle=4 cm
radius of smaller 2nd circle=2 cm