Abstract. For a point $P$ distinct from the vertices of an affinely regular $d$-gon in the affine plane $AG(2,q)$ with $q$ odd, let $n_P$ denote the number of chords through $P$. The trivial upper bound is $n_P\leq d/2$. In this paper it is shown that this can be improved to $n_P\leq d/3+2$, apart from some exceptional cases described explicitly.
AMS Subject Classification
(1991): 51E15, 51E21
affinely regular polygon,
Received July 20, 2007, and in revised form May 6, 2008, (Registered under 19/2007.)