Blocking sets of nonsecant lines to a conic in PG(2,q ), q odd A. Aguglia ∗ G. Korchm´ aros ∗ Abstract In a previous paper [1], all point set of minimum size in PG(2,q), blocking all external lines to a given irreducible conic C have been determined for every odd q. Here we obtain a similar classification for those point sets of minimum size which meet every external and tangent line to C . 1 Introduction In a joint paper [2], Boros, F¨ uredi and Kahn used a previous result of Segre and Korchm´aros [8] to prove the following theorem concerning an irreducible conic C in PG(2,q ): the minimum size of a point set B in PG(2,q ) meeting every secant and tangent of C is q + 1, and the minimum value is attained only in a few case, namely when 1. B consists of all points of an external line to C ; 2. B contains m points from C and q +1 − m points from a line ℓ. More precisely, there is an abelian linear collineation group G of order m preserving both C and ℓ such that B∩C is an orbit under G while ℓ \C is the corresponding orbit on ℓ under G which consists of all points lying on secants of B∩C . * Research supported by the Italian Ministry MURST, Strutture geometriche, combi- natoria e loro applicazioni. 1