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

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!

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}


• Hmm... I forgot to mention that I would like to change the size of the circle. \draw (0,0) circle (3); is too big now I see, so \draw (0,0) circle (2); would be fine. Quacksorry! – manooooh Jul 26 '18 at 0:06
• @manooooh Just replace all 3* by 2* and 1.5* by 1*. I deliberately did not include them in the calculation of the lengths to be able to change them easily. – user36296 Jul 26 '18 at 0:08

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) -- (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}


• +1 for using polar coordinates. Students usually don't like to learn it. – Sigur Jul 26 '18 at 1:44
• @Sigur, thank you very much! my experiences with students are similar ... – Zarko Jul 26 '18 at 6:00

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}


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}