The routine finds the intersection between two lines, a line and a circle, or two circles.

The output is obj which is assigned to a list of two points (two points of intersection), or a point (one point of intersection), or nothing (there is no point of intersection).

If the argument s is given and in case there exists two points of intersection, the names of the two points are the two elements in the list.

For more details on the point(s) of intersection, use detail.

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

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

$\mathrm{line}\left(\mathrm{l1}\,x=0\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l2}\,x+y=1\,\left[x\,y\right]\right)\:$

$\mathrm{circle}\left(c\,x^2+y^2=1\,\left[x\,y\right]\right)\:$

$\mathrm{intersection}\left(G\,\mathrm{l1}\,\mathrm{l2}\right)$

$G$

$\mathrm{intersection}\left(H\,\mathrm{l2}\,c\,\left[M\,N\right]\right)$

$\left[M\,N\right]$

$\mathrm{coordinates}\left(G\right)$

$\left[0\,1\right]$

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

$\left[\begin{array}{ll}\text{name of the object}& M\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[0\,1\right]\end{array}\,\begin{array}{ll}\text{name of the object}& N\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[1\,0\right]\end{array}\right]$

$\mathrm{circle}\left(\mathrm{c1}\,\left[\mathrm{point}\left(o\,\frac{1}{2}\,0\right)\,1\right]\,\left[x\,y\right]\right)\:$

$\mathrm{intersection}\left(\mathrm{H1}\,c\,\mathrm{c1}\,\left[U\,V\right]\right)\:$

$\mathrm{detail}\left(\mathrm{H1}\right)$

$\left[\begin{array}{ll}\text{name of the object}& U\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[\frac{1}{4}\,\frac{\sqrt{15}}{4}\right]\end{array}\,\begin{array}{ll}\text{name of the object}& V\\ \text{form of the object}& \mathrm{point2d}\\ \text{coordinates of the point}& \left[\frac{1}{4}\,-\frac{\sqrt{15}}{4}\right]\end{array}\right]$