The orthopoles of a line with respect to the four triangles formed by three out of four vertices of any quadrilateral lie on a straight line known as the orthopolar line of for the given quadrilateral (Servais 1923, McBrien 1942, Goormaghtigh 1947).
Orthopolar Line
See also
Isopolar Line, OrthopoleExplore with Wolfram|Alpha
References
Goormaghtigh, R. "Orthopolar and Isopolar Lines in the Cyclic Quadrilateral." Amer. Math. Monthly 54, 211-214, 1947.McBrien, V. O. On Some Systems of Orthopolar and Kantor Lines of Lines Referred to a Quadrangle. Washington, DC: Catholic University of America Press, 1942.Servais, C. "Sur l'orthopóle." Mathesis, p. 11, 1923.Referenced on Wolfram|Alpha
Orthopolar LineCite this as:
Weisstein, Eric W. "Orthopolar Line." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrthopolarLine.html