On the nuclei of a pointset of a finite projective plane

In this paper we study subset N(K) of a set K the points of which are not in a collinear triplet of K and prove that ¦N(K)¦≤(q+1)/2 or N(K)=K if K is a (q+1)-set of PG(2,q). We describe all the k-arcs of AG(2,q) the secants of which meet the ideal line exactly in k points.