Euler's line Equation (any triangle)

Description

In geometry, the Euler line is a line determined from any triangle that is not equilateral. It passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the nine-point circle of the triangle. In any triangle, the orthocenter, circumcenter and centroid are collinear. Let A, B, C denote the vertex angles of a not equilateral triangle, and let x : y : z be a variable point in trilinear coordinates; then an equation for the Euler line is defined by the angles of the triangle in trigonometric terms.

Related formulas

Variables

AAngle less than 180° (degree)
BAngle less than 180° (degree)
CAngle less than 180° (degree)
xX-coordinate (dimensionless)
yY-Coordinate (dimensionless)
zZ-coordinate (dimensionless)