It is for an infinite line.
Dr is the length of the segment given, distance between two point that define the line.
The distance L between this line and (0,0), where the centre of the circle is, will be L=D/Dr (
http://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line#Line_defined_by_two_points ).
Then D=L * Dr.
Which means ∆=r^2 * Dr^2 - L^2 * Dr^2.
So, the discriminant (∆, delta) is in fact square of length of given segment multiplied by the difference between the square of the distance from line to the circle and circle radius.
∆=Dr^2 * (r^2 - L^2).
Since segment length, Dr, does not affect the distance, we can assume it's 1.
Thus, ∆=r^2 - L^2
Where it is obvious that:
-if ∆ is > 0 the radius is larger than the distance of line to the circle's centre, so we have an intersection.
-If ∆ is 0, then the two are equal, and tangent.
-If ∆ is < 0, then there is no intersection since the line is further away than the circle's diameter.
Makes sense now?
