  All sets of lines providing a partition of the set of internal points to a
conic C in PG(2,q), q odd, are determined. There exist only three such linesets
up to projectivities, namely the set of all nontangent lines to C through an
external point to C, the set of all nontangent lines to C through a point in C,
and, for square q, the set of all nontangent lines to C belonging to a Baer
subplane with at least 5 common points with C. This classification theorem is
the analogous of a classical result by Segre and Korchmaros characterizing the
pencil of lines through an internal point to C as the unique set of lines, up
to projectivities, which provides a partition of the set of all noninternal
points to C. However, the proof is not analogous, since it does not rely on the
famous Lemma of Tangents of Segre. The main tools in the present paper are
certain partitions in conics of the set of all internal points to C, together
with some recent combinatorial characterizations of blocking sets of non-secant
lines, and of blocking sets of external lines.
