Extreme Points on Circumconics Induced by Isogonal Conjugates in a Triangle

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.