find three excircles of a given triangle - Maple Help

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geometry[excircle] - find three excircles of a given triangle

 Calling Sequence excircle(obj, T, n)

Parameters

 obj - list of three excircles to be created T - triangle n - (optional) a list of three elements and of the form $\left[\mathrm{c1}\left(\mathrm{o1}\right),\mathrm{c2}\left(\mathrm{o2}\right),\mathrm{c2}\left(\mathrm{o2}\right)\right]$ where c1, c2, c2, o1, o2, o3 are names.

Description

 • A circle tangent to one side of a triangle and to the extensions of the other two sides is called an excircle of the triangle.
 • The routine returns obj which is a list of three excircles of triangle T.
 • If the optional argument n is given, the names of the three excircles will be c1, c2, c3; while the names of their centers in that order will be o1, o2, o3.
 • For a detailed description of the excircles obj, use the routine detail (i.e., detail(obj))
 • Note that the routine only works if the vertices of the triangle are known.
 • The command with(geometry,excircle) allows the use of the abbreviated form of this command.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{ps}:=\mathrm{point}\left(A,1,1\right),\mathrm{point}\left(B,3,1\right),\mathrm{point}\left(C,2,4\right):$
 > $\mathrm{triangle}\left(T,\left[\mathrm{ps}\right]\right)$
 ${T}$ (1)
 > $\mathrm{excircle}\left(\mathrm{obj},T,\left[\mathrm{c1}\left(\mathrm{o1}\right),\mathrm{c2}\left(\mathrm{o2}\right),\mathrm{c3}\left(\mathrm{o3}\right)\right]\right)$
 $\left[{\mathrm{c1}}{,}{\mathrm{c2}}{,}{\mathrm{c3}}\right]$ (2)
 > $\mathrm{draw}\left(\left\{\mathrm{op}\left(\mathrm{obj}\right),T\right\},\mathrm{printtext}=\mathrm{true}\right)$