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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