Consider a triangle$\Delta ABC$ whose circumcenter is at the origin. If in $\Delta ABC$, the coordinates of the centroid $G$ are $\left(x_G,y_G\right)$ and the coordinates of the orthocenter $H$ are $\left(x_H,y_H\right)$.

Find the ratio $\dfrac{x_Hy_H}{x_Gy_G}$.

**Bonus**: Don't forget the lonely incenter!

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