Circles and straight lines

Geometry Level 5

$$Six~ points~(x_{i},y_{i}),~i=1,2,......6$$ 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 $$h+k$$

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