Summary: We show that an arrangement $\cal A$ of $n$ lines in general position in the plane has an inducing polygon of size $O(n)$. Additionally, we present a simple algorithm for finding an inducing $n$-path for $\cal A$ in $O(n \log n)$ time and an algorithm that constructs an inducing $n$-gon for a special class of line arrangements within the same time bound.