assume the radius of one circle is x, radius of the other circle is y

then:

pi*2x+pi*2y=24pi----->2pi(x+y)=24pi----->x+y=12------>y=12-x

pix^2+piy^2=80pi------->pi(x^2+y^2)=80pi------->x^2+y^2=80

plug y=12-x into x^2+y^2=80

x^2+(12-x)^2=80

x^2+144-24x+x^2=80

2x^2-24x+64=0

x^2-12x+32=0

(x-4)(x-8)=0

x1=4, x2=8

let me know if you have any questions thanks

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