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.

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

$\mathrm{ps}≔\mathrm{point}\left(A\,1\,1\right),\mathrm{point}\left(B\,3\,1\right),\mathrm{point}\left(C\,2\,4\right)\:$

$\mathrm{triangle}\left(T\,\left[\mathrm{ps}\right]\right)$

$T$

$\mathrm{excircle}\left(\mathrm{obj}\,T\,\left[\mathrm{c1}\left(\mathrm{o1}\right)\,\mathrm{c2}\left(\mathrm{o2}\right)\,\mathrm{c3}\left(\mathrm{o3}\right)\right]\right)$

$\left[\mathrm{c1}\,\mathrm{c2}\,\mathrm{c3}\right]$

$\mathrm{draw}\left(\left\{T\,\mathrm{op}\left(\mathrm{obj}\right)\right\}\,\mathrm{printtext}=\mathrm{true}\right)$