  Hyperbolic geometry plays an important role within function theory of the
disk. For example, via the Schwarz-Pick Lemma, the isometries of the unit disk
$\mathbb D$ with respect to this geometry are the conformal self-maps of
$\mathbb D$. In this elementary classroom note, we are interested in the
collection of the pseudohyperbolic disks $D_\rho(x,r)$ (with fixed radius $r$
and variable hyperbolic centers $-1<x<1$) and determine explicitely with
function theoretic tools the enveloppe of these disks.
