# STABILITY OF BROCARD POINTS

OF POLYGONS

**ADI BEN-ISRAEL AND STEPHAN FOLDES**

### Abstract:

A continuous nested sequence of similar triangles converging to the Brocard
point of a given triangle is investigated. All these triangles have the same
Brocard point. For polygons, the Brocard point need not exist, but there is
always a limit object for an analogously defined nested sequence of inner
polygons. This limit object is a Brocard point if and only if the inner
polygons are all similar to the original polygon. The similarity of two
distinct inner polygons already suffices. In that case, all the inner
polygons have the same Brocard point.