The converse of Pascal's theorem, which states that if the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie on a conic, which may degenerate into a pair of lines (Coxeter and Greitzer 1967, p. 76).
Braikenridge-Maclaurin Theorem
See also
Braikenridge-Maclaurin Construction, Conic Section, Pascal's TheoremExplore with Wolfram|Alpha
References
Coxeter, H. S. M. Projective Geometry, 2nd ed. New York: Springer-Verlag, p. 85, 1987.Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., p. 76, 1967.Referenced on Wolfram|Alpha
Braikenridge-Maclaurin TheoremCite this as:
Weisstein, Eric W. "Braikenridge-Maclaurin Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Braikenridge-MaclaurinTheorem.html