Secant line 3-secants of a finite set of points. Finiteness of the set of points is not essential in this definition, as long as each line can intersect the set in only a finite number of points. Secant line In geometry, a secant of a curve is a line that intersects the curve in at least two (distinct) points. The word "secant" comes from the Latin word "secare", meaning "to cut". In the case of a circle, a secant will intersect the circle in exactly two points and a chord is the line segment determined by these two points, that is the
Circle on the point on the circle and rotate the compass. Apollonius of Perga showed that a circle may also be defined as the set of points in a plane having a constant "ratio" (other than 1) of distances to two fixed foci, "A" and "B". (The set of points where the distances are equal is the perpendicular bisector of segment "AB", a line.) That circle is sometimes said to be drawn "about" two points. The proof is in two parts. First, one must prove that, given two foci "A" and "B" and a ratio of distances, any point "P" satisfying