Triads of Conics Associated with a Triangle
Ronaldo Garcia, Liliana Gheorghe, Peter Moses, Dan Reznik
TL;DR
This paper explores the geometric properties of triads of conics associated with a triangle, analyzing their vertices, types, and special cases such as circles and degeneracies, including the locus of centers.
Contribution
It provides a detailed analysis of the conics related to a triangle, including conditions for them to be circles or degenerate, and studies the locus of their centers.
Findings
Vertices of conic triads lie on well-known conics.
Conditions for conics to be circles or degenerate are established.
Locus of centers of degenerate conics is characterized.
Abstract
We revisit constructions based on triads of conics with foci at pairs of vertices of a reference triangle. We find that their 6 vertices lie on well-known conics, whose type we analyze. We give conditions for these to be circles and/or degenerate. In the latter case, we study the locus of their center.
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Finite Group Theory Research