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geometry

 PedalTriangle
 find the pedal triangle of a point with respect to a triangle

 Calling Sequence PedalTriangle(pT, P, T, n)

Parameters

 pT - the PedalTriangle triangle to be created P - point T - triangle n - (optional) list of three names denoting the names of three vertices of the pedal triangle

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{point}\left(A,0,0\right),\mathrm{point}\left(B,2,0\right),\mathrm{point}\left(C,1,3\right)\right]\right):$
 > $\mathrm{point}\left(P,4,4\right):$
 > $\mathrm{PedalTriangle}\left(\mathrm{pT},P,T,\left[\mathrm{A1},\mathrm{B1},\mathrm{C1}\right]\right)$
 ${\mathrm{pT}}$ (1)
 > $\mathrm{detail}\left(\mathrm{pT}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{pT}}\\ {\text{form of the object}}& {\mathrm{triangle2d}}\\ {\text{method to define the triangle}}& {\mathrm{points}}\\ {\text{the three vertices}}& \left[\left[{1}{,}{3}\right]{,}\left[\frac{{8}}{{5}}{,}\frac{{24}}{{5}}\right]{,}\left[{4}{,}{0}\right]\right]\end{array}$ (2)
 > $\mathrm{draw}\left(\left\{P,T\left(\mathrm{color}=\mathrm{blue}\right),\mathrm{pT}\left(\mathrm{color}=\mathrm{green}\right)\right\},\mathrm{printtext}=\mathrm{true}\right)$