Where is the centroid?

Geometry Level 3

A triangle has its vertices on the points \(A(2,4), B(8,-2)\) and \(C(9,9)\). The coordinate of this triangle's centroid is \(\left(\dfrac{a}{c},\dfrac{b}{c}\right)\), where \(a\), \(b\) and \(c\) are coprime integers. Find \(a+b+c\).

Bonus: Generalize the solution to find the centroid of a triangle.

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