Mad with triangle (Part 2)

Geometry Level 3

Let \(a,b,c\) denote the sides of the triangle with \(r_1, r_2, r_3\) as the radii of the excircles. Compute \( \dfrac{b-c}{r_1} + \dfrac{c-a}{r_2} + \dfrac{a-b}{r_3} \).

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