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
Circle of a sphere Let "S" be a sphere with center "O", "P" a plane which intersects "S". Draw perpendicular to "P" and meeting "P" at "E". Let "A" and "B" be any two different points in the intersection. Then "AOE" and "BOE" are right triangles with a common side, "OE", and hypotenuses "AO" and "BO" equal. Therefore, the remaining sides "AE" and "BE" are equal. This proves that all points in the intersection are the same distance from the point "E" in the plane "P", in other words all points in the intersection lie on a circle "C" with center "E". This proves