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Problem 18

If \(\tan \alpha, \tan \beta\), tan \(\gamma\) are the roots of the equation \(x^{3}-3 a x^{2}+3 b x-1=0\). Find the centroid of the triangle whose vertices are $(\tan \alpha, \cot \alpha),(\tan \beta, \cos \beta),(\tan \gamma, \cot \gamma)$.

Expert verified

The centroid of the triangle is at point \((a, b)\).

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