I'm using TikZ to create the following drawing:

So far so good, but now I'd like to center the node with the gray background vertically. Here's its code:
\setlength{\arraycolsep}{2pt}
\draw[xshift=-3cm,yshift=(current bound box.center)]
node[align=left,right,rounded corners,fill=black!10,inner sep=1ex]
{$
\left\{
\begin{array}{llc}
h &=& \overline{AF}\\
l &=& \overline{BF}\\
l'&=& \overline{AB}\\
d &=& \overline{CE}
\end{array}
\right.
$};
It's being pushed to the left by xshift, thus I could equally use yshift with a measure to center it. However, is it possible to do it dynamically (by retrieving the bounding box height)? That's, if the drawing grows, it will remain centered.
