Orthocenter, Circumcenter, and Centroid.
One Line to rule them all!

The Euler line is a straight line that passes through several important centers of a non-equilateral triangle. It contains the orthocenter, where the three altitudes meet; the circumcenter, the intersection of the midpoint perpendiculars which is also the center of the circumscribed circle (not shown); and the centroid, where the three medians intersect. These points occur in a fixed geometric relationship: the centroid lies between the circumcenter and orthocenter and divides that segment in a 1:2 ratio. The line reveals an unexpected order connecting otherwise distinct constructions within a triangle. It is used in Euclidean geometry, triangle geometry, and geometric proofs.