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
Dividing a circle into areas cross. In the second case (b), the new line crosses each of the old lines in a different point. It will be useful to know the following fact. Lemma. We can choose the new point "A" so that case "b" occurs for each of the new lines. Proof. Notice that, for the case "a", three points must be on one line: the new point "A", the old point "O" to which we draw the line, and the point "I" where two of the old lines intersect. Notice that there are "n" old points "O", and hence finitely many points "I"