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!
by
Nihar Mahajan