bisector - Maple Help

geometry

 bisector
 find the bisector of a given triangle

 Calling Sequence bisector(bA, A, ABC, P)

Parameters

 bA - A-bisector of ABC A - vertex of ABC ABC - triangle P - (optional) name

Description

 • The bisector bA of the angle at A of the triangle ABC is a line segment (or its extension) from vertex A that bisects an angle at A.
 • If the optional argument P is given, the object returned is a line segment AP where P is the intersection of the bisector at A and the opposite sides.
 • For a detailed description of the bisector bA, use the routine detail (i.e., detail(bA))
 • Note that the routine only works if the vertices of the triangle are known.
 • The command with(geometry,bisector) allows the use of the abbreviated form of this command.

Examples

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

define the line'' bisector bA

 > $\mathrm{bisector}\left(\mathrm{bA},A,\mathrm{ABC}\right)$
 ${\mathrm{bA}}$ (1)
 > $\mathrm{detail}\left(\mathrm{bA}\right)$
 assume that the names of the horizontal and vertical axes are _x and _y, respectively
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{bA}}\\ {\text{form of the object}}& {\mathrm{line2d}}\\ {\text{equation of the line}}& {-}{3}{}{\mathrm{_x}}{}\sqrt{{4}}{+}{\mathrm{_y}}{}\left({2}{}\sqrt{{10}}{+}\sqrt{{4}}\right){=}{0}\end{array}$ (2)

define the segment'' bisector bA

 > $\mathrm{bisector}\left(\mathrm{bA},A,\mathrm{ABC},n\right)$
 ${\mathrm{bA}}$ (3)
 > $\mathrm{detail}\left(\mathrm{bA}\right)$
 $\begin{array}{ll}{\text{name of the object}}& {\mathrm{bA}}\\ {\text{form of the object}}& {\mathrm{segment2d}}\\ {\text{the two ends of the segment}}& \left[\left[{0}{,}{0}\right]{,}\left[\frac{{2}{}\left(\sqrt{{10}}{+}{1}\right)}{{2}{+}\sqrt{{10}}}{,}\frac{{6}}{{2}{+}\sqrt{{10}}}\right]\right]\end{array}$ (4)