The central configuration of the planar ($N$+1)-body problem with a regular $N$-polygon

For planar ($N$+1)-body ($N$,$geq$ 2) problem with a regular $N$-polygon, under the assumption that the ($N$+1)-th body locates at the geometric center of the regular $N$-polygon, we obtain the sufficient and necessary conditions that the $N$+1 bodies can form a central configuration.