Six-Point Circles from a Triangle

Abstract

In the Euclidean plane, let $A$, $B$, $C$ be noncollinear points and $T$ be the union of the lines $AB$, $BC$, $CA$. It is shown that there is a point $P$ such that if $\tilde{T}$ is the image of $T$ by any nonrotating uniform expansion about $P$, then $T\cap \tilde{T}$ is generally a six-point set that lies on a circle.