Cyclic Product Theorems for Polygons (II) Constructions using Conic Sections

If a point Ui is chosen on each edge of a plane n -gon P , then the product of the n signed ratios in which the points Ui divide the edges of P is called a cyclic product for P . The problem is to find geometric constructions for the Ui such that, for every n -gon P , the cyclic product takes a fixed value. Many constructions are known which use lines or circles. Here we describe constructions that use conic sections.