Constructions in the Locus of Isogonal Conjugates in a Quadrilateral

2019/12/17 by Daniel Hu, Hu, Daniel
Engineering · Materials Science · #51A05 (Primary) 51N15 #51N20 (Secondary) #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #History and Overview (math.HO) #Material Properties and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1912.08296

openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given fixed distinct points A, B, C, D, we examine properties of the locus of points X for which (XA, XC), (XB, XD) are isogonal. This locus is a cubic curve circumscribing ABCD. We characterize all possible such cubics \mathcal C ∈ \mathbb R². These properties allow us to present constructions involving these cubics, such as intersections and tangent lines, using straightedge and compass.

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