  In $1967$, Vizing determined the maximum size of a graph with given order and
radius. In $1973$, Fridman answered the same question for digraphs with given
order and outradius. We investigate that question when restricting to
biconnected digraphs. Biconnected digraphs are the digraphs with a finite total
distance and hence the interesting ones, as we want to note a connection
between minimizing the total distance and maximizing the size under the same
constraints. We characterize the extremal digraphs maximizing the size among
all biconnected digraphs of order $n$ and outradius $3$, as well as when the
order is sufficiently large compared to the outradius. As such, we solve a
problem of Dankelmann asymptotically. We also consider these questions for
bipartite digraphs and solve a second problem of Dankelmann partially.
