# All Hail Euler the ruler!

Geometry Level 4

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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