If ABC is three positive numbers, and satisfies a + B + C = 18,1  a + B + 1  B + C + 1  C + a = 10  9, then what is the value of a  B + C + B  C + A + C  a + B?

1/(a+b)+1/(b+c)+1/(c+a)=10/9
a/(a+b)+a/(b+c)+a/(c+a)=(10/9)a
b/(a+b)+b/(b+c)+b/(c+a)=(10/9)b
c/(a+b)+c/(b+c)+c/(c+a)=(10/9)c
Add the above three formulas:
a/(b+c)+b/(c+a)+c/(a+b)+[a/(a+b)+b/(a+b)]+[b/(b+c)+c/(b+c)]+[c/(c+a)+a/(c+a)]=(10/9)(a+b+c)=20
a/(b+c)+b/(c+a)+c/(a+b)+3=20
a/(b+c)+b/(c+a)+c/(a+b)=17

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