The intersection graph of the disks with diameters the sides of a convex $n$-gon

Given a convex polygon of n sides, one can draw n disks (called side disks) where each disk has a different side of the polygon as diameter and the midpoint of the side as its center. The intersection graph of such disks is the undirected graph with vertices the n disks and two disks are adjacent if and only if they have a point in common. We prove that for every convex polygon this graph is planar. Particularly, for n = 5, this shows that for any convex pentagon there are two disks among the five side disks that do not intersect, which means that K5 is never the intersection graph of such five disks. For n = 6, we then have that for any convex hexagon the intersection graph of the side disks does not contain K3,3 as subgraph.