  In this work we study the intersection properties of a finite disk system in
the euclidean space. We accomplish this by utilizing subsets of spheres with
varying dimensions and analyze specific points within them, referred to as
poles. Additionally, we introduce two applications: estimating the common scale
factor for the radii that makes the re-scaled disks intersects in a single
point, this is the \v{C}ech scale, and constructing the minimal Axis-Aligned
Bounding Box (AABB) that encloses the intersection of all disks in the system.
