How to draw this customized node in TikZ?

Question

I am creating an activity-on-node project diagram for my Critical Path method lecture. I could able to create the customized node for the same as indicated in the attached image. However, I would like to customize/modify the existing node (code), to produce the modified node as indicated below the expected outcome in the attached image. Kindly help me.

The Minimal Working Example is as follows:

 \documentclass[border=12pt]{standalone}
 \usepackage{amsmath}
 \usepackage{tikz}
 \usetikzlibrary{shapes,arrows}
 \usetikzlibrary{chains}
 \usetikzlibrary{positioning}

 \tikzset{sectors/.style n args={5}{%
  circle,
  draw,
  minimum width=#4,
  append after command={%
  \pgfextra{ %
  \draw (\tikzlastnode.center) -- (\tikzlastnode.south);
  \draw (\tikzlastnode.west)   -- (\tikzlastnode.east);
  \path (\tikzlastnode.center) -- node[#5] {#1} (\tikzlastnode.north west);  
  \path (\tikzlastnode.center) -- node[#5] {#2} (\tikzlastnode.north east);  
  \path (\tikzlastnode.center) -- node[#5] {#3} (\tikzlastnode.south west); 
  \path (\tikzlastnode.center) -- node[#5] {#4} (\tikzlastnode.south east);}}}}

  \newcommand*\circled[1]{\tikz[baseline=(char.base)]{
        \node[shape=circle,draw,inner sep=1pt] (char) {#1};}}

   \begin{document}
   \begin{tikzpicture}[node distance=7cm,ultra thick]
   \node [circle split,
     draw,
     minimum width=2cm,
     append after command={%
     \pgfextra{\draw (\tikzlastnode.north) -- (\tikzlastnode.south) ;
              } 
              }]  (a)  {};
  \node[yshift=0em] at (a.center) {\LARGE \textbf{A}};  
  \node[xshift=-1.2em,yshift=1.2em] at (a.center) {\LARGE $a$}; 
  \node[xshift= 1.2em,yshift=1.2em] at (a.center) {\LARGE $b$};  
  \node[xshift=-1.2em,yshift=-1.2em] at (a.center) {\LARGE $c$}; 
  \node[xshift= 1.2em,yshift=-1.2em] at (a.center) {\LARGE $d$};  
  \end{tikzpicture}
  \end{document}

Answer 1

With some modifications on your code, the following code gives desired output.

    \documentclass[border=12pt]{standalone}
     \usepackage{amsmath}
     \usepackage{tikz}
     \usetikzlibrary{shapes,arrows}
     \usetikzlibrary{chains}
     \usetikzlibrary{positioning}

       \begin{document}
       \begin{tikzpicture}[node distance=7cm,ultra thick]
       \node [circle,
         draw,fill=white,
         minimum width=2cm,
        % append after command={%
        % \pgfextra{\draw (\tikzlastnode.north) -- (\tikzlastnode.south) ;
                % } 
                % }
                 ]  (a)  {};
\draw (a.north) -- (a.south) ; 
\draw (a.west) -- (a.east) ;            
                  \node [circle ,
         draw,fill=white,
         minimum width=0.7cm,
        % append after command={%
        % \pgfextra{\draw (\tikzlastnode.north) -- (\tikzlastnode.south) ;
                 % } 
                 % }
                  ]  (b)  {};
      \node[yshift=0em] at (a.center) {\LARGE \textbf{A}};  
      \node[xshift=-1.2em,yshift=1.2em] at (a.center) {\LARGE $a$}; 
      \node[xshift= 1.2em,yshift=1.2em] at (a.center) {\LARGE $b$};  
      \node[xshift=-1.2em,yshift=-1.2em] at (a.center) {\LARGE $c$}; 
      \node[xshift= 1.2em,yshift=-1.2em] at (a.center) {\LARGE $d$};  
      \end{tikzpicture}
      \end{document}