The Hidden Line in every triangle | Euler Line

Animation made in Manim

The Euler line of a triangle △𝐴𝐵𝐶
△ABC is a straight line that passes through several important points associated with the triangle. These points include:

Centroid (
𝐺
G): The point where the three medians of the triangle intersect.
Orthocenter (
𝐻
H): The point where the three altitudes of the triangle meet.
Circumcenter (
O): The center of the circumcircle (the circle that passes through all three vertices of the triangle).Nine-point center ( The center of the nine-point circle, which passes through nine significant points of the triangle (midpoints of the sides, feet of the altitudes, and midpoints of the segments connecting the vertices to the orthocenter).
Key Properties of the Euler Line:
In any non-equilateral triangle, G, H, O, are collinear, meaning they lie on the same line (the Euler line).
The centroid G divides the Euler line in the ratio 2:1, with G closer to the circumcenter O than to the orthocenter H.

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[thescienceandmathchannel]

O is the circumcentre(Centre of purple 🟣 circle)

H is the orthocentre (Intersection of the altitudes)

G is the centroid(intersection of the medians)