\begin{figure}[ht]
\centering
\begin{tikzpicture}[scale=2.45,>=Latex]
\fill[BMblue!8] (0,0) circle (.75);
\draw[BMorange,thick,dashed] (0,0) circle (.8);
\draw[BMblue,thick] (0,0) circle (.75);
\draw[BMgreen,thick] (0,0) circle (.125);
\draw[BMgray,densely dotted] (.09,.045) circle (.625);
\draw[very thick] (-.25,0)--(.25,0);
\fill (.09,.045) circle (.012) node[above right] {$z_*$};
\fill (0,0) circle (.01) node[below] {$t_j$};
\node[BMgreen,right] at (.8,.12) {$V_j$, radius $1/8$};
\node[BMblue,right] at (.8,.58) {$U_j$, radius $3/4$};
\node[BMorange,right] at (.8,.35) {$W_j$, radius $4/5$};
\node[align=left,right] at (.8,-.35) {Choose $|f(z_*)|=\max_{V_j}|f|$.\\
The radius-$5/8$ circle about $z_*$\\lies inside $U_j$.};
\end{tikzpicture}
\caption{The shifted Jensen construction in the $w$-plane. The thick
segment is $[t_j-1/4,t_j+1/4]$; it lies inside the radius-$1/2$ circle about
any $z_*\in V_j$. The dotted circle is one possible outer Jensen circle.
The figure is geometric and shows no numerical zero locations.}
\label{analytic:jensen-geometry}
\end{figure}