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Incenter Circles, Chromogeometry, and the Omega Triangle

Nguyen Le ; School of Mathematics and Statistics UNSW, Sydney, Australia
Norman John Wildberger orcid id ; School of Mathematics and Statistics UNSW, Sydney, Australia

Puni tekst: engleski pdf 390 Kb

str. 5-18

preuzimanja: 796



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.

Ključne riječi

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

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