Mickey Mouse?

Geometry Level 3

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

\[\frac {b-c}{r_{1}} + \frac {c-a}{r_{2}} + \frac{a-b}{r_{3}}.\]

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