# 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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