# Finding a point of intersection of two objects in the plane: single_inter line_inter

### 13.6.6 Finding a point of intersection of two objects in the plane: single_inter line_inter

See Section 14.4.3 for single points of intersection of objects in space.

The single_inter command finds an intersection point of two geometric objects.
line_inter is a synonym for single_inter

- single_inter takes two mandatory arguments and one optional argument.
  - obj1, obj2, two geometric objects.
  - Optionally, pt, a point or list of points.
  line_inter(obj1,obj2 ⟨pt⟩) returns one of the points of intersection of obj1 and obj2.
  If pt is a single point, then the command returns the point of intersection closest to pt.
  If pt is a list of points, then the command tries to return a point not in pt.

#### Example.

The command circle(0,1) creates the unit circle and line(-1,i) creates a line, these two objects intersect at the points (−1,0) and (0,1).
Input:

single_inter(circle(0,1),line(-1,i))

Output:

which is the point (−1,0).
Input:

single_inter(circle(0,1),line(-1,i),[-1])

Output:

which is the point (0,1). Similarly, since this second point of intersection is closest to (0,1/2), entering:
Input:

single_inter(circle(0,1),line(-1,i),i/2)

also draws the second point.