TL;DR
This paper explores the properties of Omega circles passing through Brocard points, revealing their similarities to orthocenter circles and their role in understanding indirectly similar triangles.
Contribution
It introduces new properties of Omega circles and their relation to triangles inscribed in the circumcircle, completing the study on indirectly similar triangles.
Findings
Omega circles share properties with orthocenter circles.
Circles through median-orthocentroidal intersections relate to directly similar triangles.
The work concludes the analysis of indirectly similar triangles.
Abstract
Circles through the Brocard points (Omega circles) share nearly all the properties of circles through the orthocentre including the fact that key triangles inscribed in them are indirectly similar to triangles inscribed in the circumcircle. Properties of Omega circles are described in this article, thereby concluding our work on indirectly similar triangles. It is also shown that the three points where the medians intersect the orthocentroidal circle are such that circles through these points carry triangles directly similar to triangles inscribed in the circumcircle.
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Taxonomy
TopicsOptics and Image Analysis