  In their seminal work, Danzer (1956, 1986) and Stach\'{o} (1981) established
that every set of pairwise intersecting disks in the plane can be stabbed by
four points. However, both these proofs are non-constructive, at least in the
sense that they do not seem to imply an efficient algorithm for finding the
stabbing points, given such a set of disks $D$. Recently, Har-Peled \etal
(2018) presented a relatively simple linear-time algorithm for finding five
points that stab $D$. We present an alternative proof (and the first in
English) to the assertion that four points are sufficient to stab $D$.
Moreover, our proof is constructive and provides a simple linear-time algorithm
for finding the stabbing points. As a warmup, we present a nearly-trivial
liner-time algorithm with an elementary proof for finding five points that stab
$D$.
