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Circle-Line Intersection
source link: https://mathworld.wolfram.com/Circle-LineIntersection.html
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Circle-Line Intersection
An (infinite) line determined by two points 
and 
may intersect
a circle of radius 
and center (0,
0) in two imaginary points (left figure), a degenerate single point (corresponding
to the line being tangent to the circle; middle figure), or two real points (right
figure).
In geometry, a line meeting a circle in exactly one point is known as a tangent line, while a line meeting a circle in exactly two points in known as a secant line (Rhoad et al. 1984, p. 429).
Defining
 |  |  | |
 |  |  | |
 |  |  | |
 |  |  |
gives the points of intersection as
 |  |  | |
 |  |  |
where the function 
is defined
as
 |
The discriminant
 |
therefore determines the incidence of the line and circle, as summarized in the following table.
 | incidence |
 | no intersection |
 | tangent |
 | intersection |
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