Secant line 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 interval on a secant whose endpoints are these points. A straight line can intersect a circle in two, one or zero points. A line intersecting in two points is called a "secant line", in one
Area of a circle the excess amount. Inscribe a square in the circle, so that its four corners lie on the circle. Between the square and the circle are four segments. If the total area of those gaps, "G", is greater than "E", split each arc in half. This makes the inscribed square into an inscribed octagon, and produces eight segments with a smaller total gap, "G". Continue splitting until the total gap area, "G", is less than "E". Now the area of the inscribed polygon, "P" = "C" − "G", must be greater than that of the triangle. But this forces a contradiction,