User:MathInclined/sandbox

$\usepackage{tikz}

 \def\firstcircle{(90:1.75cm) circle (2.5cm)}
 \def\secondcircle{(210:1.75cm) circle (2.5cm)}
 \def\thirdcircle{(330:1.75cm) circle (2.5cm)}
 \begin{document}
   \begin{tikzpicture}
     \begin{scope}
   \clip \secondcircle;
   \fill[cyan] \thirdcircle;
     \end{scope}
     \begin{scope}
   \clip \firstcircle;
   \fill[cyan] \thirdcircle;
     \end{scope}
     \draw \firstcircle node[text=black,above] {$A$};
     \draw \secondcircle node [text=black,below left] {$B$};
     \draw \thirdcircle node [text=black,below right] {$C$};
   \end{tikzpicture}$