  We study the problem of arranging a set of $n$ disks with prescribed radii on
$n$ rays emanating from the origin such that two neighboring rays are separated
by an angle of $2\pi/n$. The center of the disks have to lie on the rays, and
no two disk centers are allowed to lie on the same ray. We require that the
disks have disjoint interiors, and that for every ray the segment between the
origin and the boundary of its associated disk avoids the interior of the
disks. Let $\r$ be the sum of the disk radii. We introduce a greedy strategy
that constructs such a disk arrangement that can be covered with a disk
centered at the origin whose radius is at most $2\r$, which is best possible.
The greedy strategy needs O(n) arithmetic operations.
  As an application of our result we present an algorithm for embedding
unordered trees with straight lines and perfect angular resolution such that it
can be covered with a disk of radius $n^{3.0367}$, while having no edge of
length smaller than 1. The tree drawing algorithm is an enhancement of a recent
result by Duncan et al. [Symp. of Graph Drawing, 2010] that exploits the
heavy-edge tree decomposition technique to construct a drawing of the tree that
can be covered with a disk of radius $2 n^4$.
