  Let $\mathcal{P}$ be a simple polygon with $m$ vertices and let $P$ be a set
of $n$ points inside $\mathcal{P}$. We prove that there exists, for any
$\varepsilon>0$, a set $\mathcal{C} \subset P$ of size $O(1/\varepsilon^2)$
such that the following holds: for any query point $q$ inside the polygon
$\mathcal{P}$, the geodesic distance from $q$ to its furthest neighbor in
$\mathcal{C}$ is at least $1-\varepsilon$ times the geodesic distance to its
further neighbor in $P$. Thus the set $\mathcal{C}$ can be used for answering
$\varepsilon$-approximate furthest-neighbor queries with a data structure whose
storage requirement is independent of the size of $P$. The coreset can be
constructed in $O\left(\frac{1}{\varepsilon} \left( n\log(1/\varepsilon) +
(n+m)\log(n+m)\right) \right)$ time.
