Journal for Geometry and Graphics 24 (2020), No. 1, 009--028
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 R2 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.
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