
Journal for Geometry and Graphics 24 (2020), No. 1, 009028 Copyright Heldermann Verlag 2020 Constructions in the Locus of Isogonal Conjugates for a Quadrilateral Daniel Hu Los Altos High School, 201 Almond Avenue, Los Altos, CA 94022, U.S.A. daniel.b.hu@gmail.com Given fixed distinct points A, B, C, D, we examine properties of and constructions involving the cubic plane curve locus of points X for which (XA, XC), (XB, XD) are isogonal. We establish a necessary and sufficient condition for all cubics Cu in real plane R^{2} such that there exist corresponding points A, B, C, D in Cu for which Cu is this exact locus. Keywords: isogonal cubic, focal cubic, isogonal conjugate, excellent point, spiral center of quadrangle, Miquel point. MSC: 51N20; 51N35, 51N15. [ Fulltextpdf (1218 KB)] 