How to divide a circle into 3 parts with text using tikzpicture environment

Question

I would like to draw a circle divided into 3 parts with text inside, same in each of the three parts (in the middle), using tikzpicture environment. Something like:

All the circle and its interior must be black, and the text of each part must be using \(...\).

MWE:

\documentclass{article}
\usepackage[spanish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}

\begin{center}
    \begin{tikzpicture}
        \draw (0,0) circle (3);

    \end{tikzpicture}
\end{center}
\end{document}

Thank you!

Answer 1

The interception points of the lines with the circle can easily be calculated using trigonometric functions. Once these points are known, drawing is straight forward:

\documentclass{article}
\usepackage[spanish]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}

\begin{document}

\begin{center}
    \begin{tikzpicture}
        \draw (0,0) circle (3);
                \draw (0,3) -- (0,0) -- (3*0.866,-3*0.5) (0,0) -- (-3*0.866,-3*0.5);
                \node at (0,-1.5) {$\{A,B\}$};
                \node at (1.5*0.866,1.5*0.5) {$\{A,B\}$};
                \node at (-1.5*0.866,1.5*0.5) {$\{A,B\}$};
    \end{tikzpicture}
\end{center}
\end{document}

Answer 2

an alternative:

• used polar coordinates

• define radius of circle and with it also calculated distances of nodes from circle centre

  \documentclass[tikz, margin=3mm]{standalone}
  \usepackage[spanish]{babel}
  \usepackage[T1]{fontenc}
  \usetikzlibrary{babel}
  
  \begin{document}
      \begin{tikzpicture}
  \def\R{3cm} % defined radius of circle
  \draw (0,0) circle[radius=\R];
  \draw (0,0) -- (90:\R)    (0,0) -- (210:\R)     (0,0) -- (330:\R);
  %
  \node at ( 30:\R/2) {\(\{A,B\}\)};
  \node at (150:\R/2) {\(\{A,B\}\)};
  \node at (270:\R/2) {\(\{A,B\}\)};
      \end{tikzpicture}
  \end{document}
  

Answer 3

I copied some Zako's code. I use tkz-euclide. The points B and C are found with rotation.

\documentclass[border=1.5mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tkz-euclide,amsmath} 
\usetkzobj{all} 
\tikzset{line/.style = {thick}}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\def\R{2}
\tkzDefPoint(0,0){O}\tkzDefPoint(90:\R){A}
\tkzDefPointsBy[rotation=center O angle 360/3](A,B){B,C}
\tkzDrawCircle[R](O,\R cm)
\tkzDrawSegments[line](O,A O,B O,C)
\node at ( 30:\R/2) {\(\{A,B\}\)};
\node at (150:\R/2) {\(\{A,B\}\)};
\node at (270:\R/2) {\(\{A,B\}\)};
\end{tikzpicture}
\end{document}

Answer 4

Nobody proposed a circular node with its angular anchors.

\documentclass[tikz,border=2mm]{standalone} 

\begin{document}
\begin{tikzpicture}
\node[circle,draw, minimum width=4cm, outer sep=0pt] (a) {};
\foreach \i in {90,210,330}
    \draw (a.center)--(a.\i);

\foreach \i/\j in {30/{A,B},150/{E,F},270/{C,D}}
    \path (a.center) -- node {$\{\j\}$} (a.\i); 
\end{tikzpicture}
\end{document}