Where is the centroid?

Geometry Level 3

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

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

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