Aire, p\'erim\`etre et polygones cocycliques

This paper provides (in french) a framework for an alternative demonstration of result of Khimshiashvili and Panina on the characterization of critical points of the area on the manifold of polygons with fixed sidelengths as being the cocyclical polygons. Other problems of the same class, with less constraints, are also alluded to and a numerical scheme for computing the associated gradient descent is described.