intersection - Maple Help

geometry

 intersection
 find the intersections between two lines, a line and a circle, or two circles

 Calling Sequence intersection(obj, f, g, s)

Parameters

 obj - name f, g - the lines or circles s - (optional) list of two names

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{geometry}\right):$
 > $\mathrm{line}\left(\mathrm{l1},x=0,\left[x,y\right]\right),\mathrm{line}\left(\mathrm{l2},x+y=1,\left[x,y\right]\right):$
 > $\mathrm{circle}\left(c,{x}^{2}+{y}^{2}=1,\left[x,y\right]\right):$
 > $\mathrm{intersection}\left(G,\mathrm{l1},\mathrm{l2}\right)$
 ${G}$ (1)
 > $\mathrm{intersection}\left(H,\mathrm{l2},c,\left[M,N\right]\right)$
 $\left[{M}{,}{N}\right]$ (2)
 > $\mathrm{coordinates}\left(G\right)$
 $\left[{0}{,}{1}\right]$ (3)
 > $\mathrm{detail}\left(H\right)$
 $\left[\begin{array}{ll}{\text{name of the object}}& {M}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{0}{,}{1}\right]\end{array}{,}\begin{array}{ll}{\text{name of the object}}& {N}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[{1}{,}{0}\right]\end{array}\right]$ (4)
 > $\mathrm{circle}\left(\mathrm{c1},\left[\mathrm{point}\left(o,\frac{1}{2},0\right),1\right],\left[x,y\right]\right):$
 > $\mathrm{intersection}\left(\mathrm{H1},c,\mathrm{c1},\left[U,V\right]\right):$
 > $\mathrm{detail}\left(\mathrm{H1}\right)$
 $\left[\begin{array}{ll}{\text{name of the object}}& {U}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[\frac{{1}}{{4}}{,}\frac{\sqrt{{15}}}{{4}}\right]\end{array}{,}\begin{array}{ll}{\text{name of the object}}& {V}\\ {\text{form of the object}}& {\mathrm{point2d}}\\ {\text{coordinates of the point}}& \left[\frac{{1}}{{4}}{,}{-}\frac{\sqrt{{15}}}{{4}}\right]\end{array}\right]$ (5)