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
Concyclic points the sides of a triangle, then the six points of intersection of the lines and the sides of the triangle are concyclic, in what is called the Lemoine circle. The van Lamoen circle associated with any given triangle formula_6 contains the circumcenters of the six triangles that are defined inside formula_6 by its three medians. A triangle's circumcenter, its Lemoine point, and its first two Brocard points are concyclic, with the segment from the circumcenter to the Lemoine point being a diameter. A polygon is defined to be cyclic if its vertices are all concyclic. For example, all the vertices