Stability of Brocard points of polygons (Q5928684)

The Brocard point of a triangle \(A_1A_2A_3\subset E^2\) is the unique point \(B\) within \(A_1A_2A_3\) yielding for all \(i\) modulo 3 equal angles between \(A_iB\) and \(A_iA_{i+1}\).NEWLINENEWLINENEWLINEThe authors consider a continuous nested sequence of similar triangles converging to a Brocard point of a given one, all having the same Brocard point. Although for polygons with more vertices the Brocard point need not exist, one might consider a certain limit object for an analogously defined nested sequence of inner polygons. It is shown that this is a Brocard point iff all the inner polygons and the starting polygon are similar to each other.