  Our aim is to prove a Poncelet type theorem for a line configuration on the
complex projective. More precisely, we say that a polygon with 2n sides joining
2n vertices A1, A2,..., A2n is well inscribed in a configuration Ln of n lines
if each line of the configuration contains exactly two points among A1, A2,
..., A2n. Then we prove : "Let Ln be a configuration of n lines and D a smooth
conic in the complex projective plane. If it exists one polygon with 2n sides
well inscribed in Ln and circumscribed around D then there are infinitely many
such polygons. In particular a general point in Ln is a vertex of such a
polygon." We propose an elementary proof based on Fr\'egier's involution. We
begin by recalling some facts about these involutions. Then we explore the
following question : When does the product of involutions correspond to an
involution? It leads to Pascal theorem, to its dual version proved by
Brianchon, and to its generalization proved by M\"obius.
