On the mean length of the diagonals of an $n$-gon

P. Erdős [1] conjectured that the mean length of the diagonals of a convex n-gon with perimeter L is maximal iff n/2 vertices are concentrated in a point A and the remaining n/2 vertices in a point B whose distance is L/2 in case of n = 2k. If n = 2k + 1, then k and k + 1 vertices are concentrated in A and B , respectively, in the extremal figure. The minimum is attained when n − 1 vertices are concentrated in A and a single one in B .