The Quadrilateral Nagel Point, The Behavior of Splitters, and a Special Line

2026/03/23 by Thomas E. Cooper
Mathematics · #Mathematics and Applications #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows

paper · doi:10.1080/00029890.2026.2621647

Abstract

In this article, we use the four semi-excircles of a general convex quadrilateral to define a Nagel point, and we examine the behavior of certain segments that divide the perimeter of a convex quadrilateral in half. Most notably, we classify all quadrilaterals that have concurrent splitters, and we find that a certain set of intersections involving the splitters are collinear with the Nagel point and the intersection of the diagonals in any convex quadrilateral.

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