Wikipedia has a nice article on centroids which contains the solution to your type of problem:
Centroid - Wikipedia, the free encyclopedia
hence mid-point X = (1, 6)
Then use points X(1,6) and C(7,6) to work out the equation for line XC:
and simplify it into the form of
Ax + By + C = 0 or
y = mx + c
where A, B, C, m and c are positive/negative constants or coefficients.
do the same for AZ and BY, and finally put all the three equations for XC, AZ and BY together and solve it for the values of x and y, which are the coordinates of the centriod O.