The pedal triangle pT of point P with respect to triangle T is the triangle formed by the feet of the perpendiculars drawn from point P to the sides of T (or their extensions).

If the optional argument is given and is a list of three names, these three names will be assigned to the three vertices of the pedal triangle pT

For a detailed description of the pedal triangle pT, use the routine detail (i.e., detail(pT))

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

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

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

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

$\mathrm{point}\left(P\,4\,4\right)\:$

$\mathrm{PedalTriangle}\left(\mathrm{pT}\,P\,T\,\left[\mathrm{A1}\,\mathrm{B1}\,\mathrm{C1}\right]\right)$

$\mathrm{pT}$

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

$\begin{array}{ll}\text{name of the object}& \mathrm{pT}\\ \text{form of the object}& \mathrm{triangle2d}\\ \text{method to define the triangle}& \mathrm{points}\\ \text{the three vertices}& \left[\left[1\,3\right]\,\left[\frac{8}{5}\,\frac{24}{5}\right]\,\left[4\,0\right]\right]\end{array}$

$\mathrm{draw}\left(\left\{P\,T\left(\mathrm{color}=\mathrm{blue}\right)\,\mathrm{pT}\left(\mathrm{color}=\mathrm{green}\right)\right\}\,\mathrm{printtext}=\mathrm{true}\right)$