  A long-standing open conjecture of Branko Gr\"unbaum from 1972 states that
any simple arrangement of $n$ pairwise intersecting pseudocircles in the plane
can have at most $2n-2$ digons. Agarwal et al. proved this conjecture for
arrangements of pairwise intersecting pseudocircles in which there is a common
point surrounded by all pseudocircles. Recently, Felsner, Roch and Scheucher
showed that Gr\"unbaum's conjecture is true for arrangements of pairwise
intersecting pseudocircles in which there are three pseudocircles every pair of
which create a digon. In this paper we prove this over 50-year-old conjecture
of Gr\"unbaum for any simple arrangement of pairwise intersecting circles in
the plane.
