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Secant line: Wikis

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Common lines and line segments on a circle, including the secant line

A secant line of a curve is a line that (locally) intersects two points on the curve. The word secant comes from the Latin secare, to cut.

It can be used to approximate the tangent to a curve, at some point f. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P, assuming there is just one. As a consequence, one could say that the limit of the secant's slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative. A chord is the portion of a secant that lies within the curve.


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