Let [Formula: see text] be a planar Poisson point process of intensity [Formula: see text]. We give a new proof that the expected length of the Voronoi path between [Formula: see text] and [Formula: see text] in the Delaunay triangulation associated with [Formula: see text] is [Formula: see text] when [Formula: see text] goes to infinity; and we also prove that the variance of this length is [Formula: see text]. We investigate the length of possible shortcuts in this path, and define a shortened Voronoi path whose expected length can be expressed as an integral that is numerically evaluated to [Formula: see text]. The shortened Voronoi path has the property to be locally defined; and is shorter than the previously known locally defined paths in Delaunay triangulation such as the upper path whose expected length is [Formula: see text].