  We provide a simple proof of the existence of a planar separator by showing
that it is an easy consequence of the circle packing theorem. We also reprove
other results on separators, including:
  (A) There is a simple cycle separator if the planar graph is triangulated.
Furthermore, if each face has at most $d$ edges on its boundary, then there is
a cycle separator of size O(sqrt{d n}).
  (B) For a set of n balls in R^d, that are k-ply, there is a separator, in the
intersection graph of the balls, of size O(k^{1/d}n^{1-1/d}).
  (C) The k nearest neighbor graph of a set of n points in R^d contains a
separator of size O(k^{1/d} n^{1-1/d}).
  The new proofs are (arguably) significantly simpler than previous proofs.
