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Extreme Points on Circumconics Induced by Isogonal Conjugates in a Triangle

2019/12/18 by Daniel Hu, Hu, Daniel
Mathematics · #51A05 (Primary) 51N15 #51N20 (Secondary) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1912.08330

openalex publication_date 2019/12/18 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

We first introduce a configuration of arbitrary isogonal conjugates related to a known property concerning the spiral center of two pairs of isogonal conjugates. We then consider a special case where two conics are tangent at exactly two points. Finally, we apply the discoveries made in both configurations to state a general result concerning the extreme points (those lying on either the major or minor axis) of certain circumconics of a triangle.

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