A note on lenses in arrangements of pairwise intersecting circles in the plane

Let be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by is at most $2n-2$. This bound is tight. Furthermore, if no two circles in touch, then the geometric graph G on the set of centers of the circles in whose edges correspond to the lenses generated by does not contain pairs of avoiding edges. That is, G does not contain pairs of edges that are opposite edges in a convex quadrilateral. Such graphs are known to have at most $2n-2$ edges.