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geometry

 EulerLine
 find the Euler line of a given triangle

 Calling Sequence EulerLine(Ell, T)

Parameters

 Ell - the name of the Euler line T - triangle

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,2,0\right),\mathrm{point}\left(C,1,3\right)\right],\left[a,b\right]\right):$
 > $\mathrm{EulerLine}\left(\mathrm{Ell},T\right)$
 ${\mathrm{Ell}}$ (1)
 > $\mathrm{detail}\left(\mathrm{Ell}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{Ell}}\\ {\text{form of the object}}& {\mathrm{line2d}}\\ {\text{equation of the line}}& {-}\frac{{2}}{{3}}{+}\frac{{2}{}{a}}{{3}}{=}{0}\end{array}$ (2)