If the centroid of the triangle formed by the points \( A(a, b), B(b, c) \) and \( C(c, a) \) is...

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If the centroid of the triangle formed by the points \( A(a, b), B(b, c) \) and \( C(c, a) \) is at the origin. What is the value of \( \frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b} ? \)
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