Original scientific paper

Incenter Circles, Chromogeometry, and the Omega Triangle

Nguyen Le ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman John Wildberger orcid.org/0000-0003-3503-6495 ; School of Mathematics and Statistics UNSW, Sydney, Australia

Abstract

Chromogeometry brings together planar Euclidean geometry, here called blue geometry, and two relativistic geometries, called red and green. We show that if a triangle has four blue Incenters and four red Incenters, then these eight points lie on a green circle, whose center is the green Orthocenter of the triangle, and similarly for the other colours. Tangents to the incenter circles yield interesting additional standard quadrangles and concurrencies. The proofs use the framework of rational trigonometry together with standard coordinates for triangle geometry, while a dilation argument allows us to extend the results also to Nagel and Speiker points.

Keywords

triangle geometry; incenter circles; rational trigonometry; chromogeometry; four-fold symmetry; Nagel points; Spieker points; Omega triangle

Hrčak ID:

133842

URI

https://hrcak.srce.hr/133842

Publication date:

30.1.2015.

Article data in other languages: croatian

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