  Let $P$ be a path graph of $n$ vertices embedded in a metric space. We
consider the problem of adding a new edge to $P$ to minimize the radius of the
resulting graph. Previously, a similar problem for minimizing the diameter of
the graph was solved in $O(n\log n)$ time. To the best of our knowledge, the
problem of minimizing the radius has not been studied before. In this paper, we
present an $O(n)$ time algorithm for the problem, which is optimal.
