Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2017, Director: Eduardo Casas Alvero[en] This project consists in a revision and extension of a classic result, Waring’s theorem, about the barycenter of the intersection points of two plane algebraic curves. The theorem arises from the study of the parts with highest degree of the equation of a curve, which are completely determined by the barycentric parallel lines of the groups of asymptotes. Among other consequences of Waring’s theorem we study a result, due to Chasles, about the barycenter of the contact points of parallel tangent lines to a plane curve.