If the orthocentre and the centroid of a triangle are at (5,2,-6) and (9,6,–4) respectively then its circumcentre is

Given that the orthocenter and the centroid of the triangle $\left(5,2,-6\right)$and $\left(9,6,-4\right)$

Let the circumcenter will be $S\left(x,y,z\right)$

We know that $G$ divides $OS$ in the ratio $2:1$ internally

Hence, $\left(9,6,-4\right)=\left(\frac{2x+5}{3},\frac{2y+2}{3},\frac{2z-6}{3}\right)$

It implies that 

$\begin{array}{rcl}\frac{2x+5}{3}& =& 9\\ 2x+5& =& 27\\ 2x& =& 22\\ x& =& 11\end{array}$

and 

$\begin{array}{rcl}\frac{2y+2}{3}& =& 6\\ 2y+2& =& 18\\ 2y& =& 16\\ y& =& 8\end{array}$

Hence, the circumcenter is $\left(11,8,-3\right)$