Mickey Mouse?

Geometry Level 3

If a,b,a,b, and cc are the side lengths of ABC\triangle ABC opposite to angles A,B,A,B, and C,C, respectively, and r1,r2,r_{1},r_{2}, and r3r_{3} are the corresponding exradii, then find the value of

bcr1+car2+abr3.\frac {b-c}{r_{1}} + \frac {c-a}{r_{2}} + \frac{a-b}{r_{3}}.

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