Relationships Between Six Excircles
Stanley Rabinowitz
TL;DR
This paper explores the relationships between the radii of excircles of smaller triangles formed within a larger triangle when a point inside it is connected by cevians.
Contribution
It introduces new theorems linking excircle radii of subdivided triangles created by cevians through an interior point.
Findings
Derived formulas relating excircle radii of subdivided triangles.
Established geometric relationships between excircles and cevians.
Provided proofs for new theorems on excircle configurations.
Abstract
If is a point inside , then the cevians through divide into smaller triangles of various sizes. We give theorems about the relationship between the radii of certain excircles of some of these triangles.
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Taxonomy
TopicsMathematics and Applications · Limits and Structures in Graph Theory · Point processes and geometric inequalities