On the existence and constructibility of inscribed polygons (Q1315111)

The author shows: (1) If \(n>2\) is a natural number and \(a_ 1,\ldots,a_ n\) are positive reals, a polygon inscribed in a circle with sides \(a_ 1,\ldots,a_ n\) exists if and only if \(2a_ i<\sum^ n_{j=1}a_ j\) for all \(i\). (2) There is no construction by compasses and ruler if \(n\geqq 5\).