  We prove that if $C$ is a reflexive smooth plane curve of degree $d$ defined
over a finite field $\mathbb{F}_q$ with $d\leq q+1$, then there is an
$\mathbb{F}_q$-line $L$ that intersects $C$ transversely. We also prove the
same result for non-reflexive curves of degree $p+1$ and $2p+1$ where
$q=p^{r}$.
