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geometry

 SimsonLine
 find the Simson line of a given triangle with respect to a given point on the circumcircle of the triangle

 Calling Sequence SimsonLine(sl, N, T)

Parameters

 sl - the name of the Simson line N - point on the circumcircle T - triangle

Description

 • The feet of the perpendiculars from any point N on the circumcircle of a triangle T to the sides of the triangle are collinear. The line of collinearity is called the Simson line of the point N for the triangle T
 • For a detailed description of the Simson line sl, use the routine detail (i.e., detail(sl))
 • Note that the routine only works if the vertices of triangle T are known.
 • The command with(geometry,SimsonLine) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{point}\left(A,-1,0\right),\mathrm{point}\left(B,1,0\right),\mathrm{point}\left(C,0,1\right)\right]\right):$
 > $\mathrm{point}\left(N,\frac{1}{\mathrm{sqrt}\left(2\right)},\frac{1}{\mathrm{sqrt}\left(2\right)}\right):$
 > $\mathrm{SimsonLine}\left(\mathrm{sl},N,T\right)$
 ${\mathrm{sl}}$ (1)
 > $\mathrm{detail}\left(\mathrm{sl}\right)$
 assume that the names of the horizontal and vertical axes are _x and _y, respectively
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{sl}}\\ {\text{form of the object}}& {\mathrm{line2d}}\\ {\text{equation of the line}}& {\mathrm{_x}}{}\left({-}\frac{{1}}{{2}}{-}\frac{\sqrt{{2}}}{{2}}\right){-}\frac{{\mathrm{_y}}}{{2}}{+}\frac{\left(\frac{\sqrt{{2}}}{{2}}{+}\frac{{1}}{{2}}\right){}\sqrt{{2}}}{{2}}{=}{0}\end{array}$ (2)
 > $\mathrm{draw}\left(\left\{N,T,\mathrm{sl}\right\}\right)$