I'm pleased to see that Altermundus has posted a method using tkz-euclide.  There were two preliminary things that I wanted to say about this diagram and one of them was that if you're doing geometrical diagrams then you should take a look at the tkz packages (I don't know much about them myself but I've seen Altermundus do some pretty amazing diagrams here using them).

The other thing I wanted to say was that whilst it is tempting to use nodes to draw particular shapes, it has its drawbacks.  Nodes are designed to hold text and some of their behaviours stem from that - in particular how they are affected by transformations.  It is possible to circumvent these behaviours, but you do have to know how.

That's not an answer, though, more of a comment.

I do have an answer for you and one that doesn't use nodes.

\documentclass{article}
%\url{http://tex.stackexchange.com/q/35266/86}
\usepackage{tikz}
\usetikzlibrary{calc}

\makeatletter
% This provides a translation from numbers to letters for labelling
% the vertices
\newcommand\numToAlpha[1]{\@Alph#1}
\makeatother

\begin{document}
\begin{tikzpicture}
% This draws the circle
\draw[dashed] (0,0) circle[radius=3cm];
% This draws,fills and labels the polygon
\draw[ultra thick,blue,fill=blue!25] (0,0)
% Set the number of sides
    let \n1=7 in
% We start so that the second line is the lower horizontal
% This means that the first vertex that we label is the left
% end of the lower horizontal
    ({-90 - 3*360/(2*\n1)}:3)
% Now we iterate over the edges
    \foreach \l in {1,...,\n1} {
% This saves our next angle (as we use it twice)
      let \n2={-90 + (2 * \l - 3) * 360/(2 * \n1)} in
% This draws the edge and labels it
% As our first edge is actually the last one, our label needs
% shifting round (modulo the number of edges)
      -- node[auto,swap,text=black] {\pgfmathparse{int(Mod(\l-2,\n1)+1)}\pgfmathresult}
% This is the endpoint of the edge
     (\n2:3)
% This is the label at the endpoint, we could have chosen to
% label the start of the edge, but then the offset would have
% been slightly more complicated.
% We also save these nodes since we'll want two of them later
     node[label={[text=black]\n2:{\numToAlpha{\l}}}] (\numToAlpha{\l}) {}
    };
% This is our point "S", I chose coordinates at random
\fill (1,.5) circle[radius=2pt] coordinate (S) node[above] {S};
% This draws the dashed lines to the edge
\draw[dashed] (A) -- (S) -- (B);
\begin{scope}
% My method for drawing the angle is sneaky: I clip a circle
% against the dashed path
\clip (A) -- (S) -- (B);
\draw[blue,ultra thick,fill=blue!50] (S) circle[radius=1cm];
\end{scope}
% Then to position the alpha, I use an invisible path that
% goes from S to the midpoint of A-B
\path ($(S)!1.2cm!($(B)!.5!(A)$)$) node {\(\alpha\)};
% Finally, we label the edge A-B with its distance
\path (A) -- node[auto] {\(A B = 16m\)} (B);
\end{tikzpicture}
\end{document}


Here's the result:



(Forgot a text=black.  The code's correct but the numbers in the picture are blue instead of black.)

Hexagon with exscribed triangle
I am building a new testing environment, and in the process I have noticed that the Forefront services are missing from the Service Manager. Is there a way to add these services? This is the first time I have seen these missing. I am a local admin on the server. We are running Server 2008 R2 Enterprise with SP1
