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This paper provides (in french) a framework for an alternative demonstrationof result of Khimshiashvili and Panina on the characterization of criticalpoints of the area on the manifold of polygons with fixed sidelengths as beingthe cocyclical polygons. Other problems of the same class, with lessconstraints, are also alluded to and a numerical scheme for computing theassociated gradient descent is described.

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