Omega Circles

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.