Circles and straight lines

$Six~ points~(x_{i},y_{i}),~i=1,2,......6$ are taken on the circle $x^2+y^2=4$ such that $\displaystyle \sum _{i=1}^{6}x_{i}=8~and~\displaystyle \sum_{i=1}^{6}y_{i}=4$ . The line segment joining $orthocentre$ of the triangle made by any three points and the $centroid$ of the triangle made by other three points passes through a fixed point $(h,k)$ , then find $h+k$