  Let $(N,\Phi)$ be a circular Ferrero pair. We define the disk with center $b$
and radius $a$, $\mathcal{D}(a;b)$, as \[\mathcal{D}(a;b)=\{x\in \Phi(r)+c\mid
r\neq 0,\ b\in \Phi(r)+c,\ |(\Phi(r)+c)\cap (\Phi(a)+b)|=1\}.\] We prove that
in the field-generated case there are many analogies with the Euclidean
geometry. Moreover, if $\mathcal{B}^{\mathcal{D}}$ is the set of all disks,
then, in some interesting cases, we show that the incidence structure
$(N,\mathcal{B}^{\mathcal{D}},\in)$ is actually a balanced incomplete block
design.
