The Euler line Ell of triangle T is the line on which the orthocenter, centroid and circumcenter lie.

For a detailed description of the Euler line, use the routine detail (e.g., detail(Ell))

Note that the routine only works if the vertices of triangle T are known.

The command with(geometry,EulerLine) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{triangle}\left(T\,\left[\mathrm{point}\left(A\,0\,0\right)\,\mathrm{point}\left(B\,2\,0\right)\,\mathrm{point}\left(C\,1\,3\right)\right]\,\left[a\,b\right]\right)\:$

$\mathrm{EulerLine}\left(\mathrm{Ell}\,T\right)$

$\mathrm{Ell}$

$\mathrm{detail}\left(\mathrm{Ell}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{Ell}\\ \text{form of the object}& \mathrm{line2d}\\ \text{equation of the line}& -\frac{2}{3}+\frac{2a}{3}=0\end{array}$