Releux triangle

A well-known classic field of mathematics is geometry. You may know Euclidean geometry from school, with constructions by compass and ruler. Math teachers may be very interested in drawing geometry constructions and explanations. Underlying constructions can help us with general drawings where we would need intersections and tangents of lines and circles, even if it does not look like geometry.

So, here, we will remember school geometry drawings. We will use the tkz-euclide package, which works on top of TikZ.

We will construct an equilateral triangle. Then we extend it to get a Releux triangle, and add annotations.

The code is fully explained in the LaTeX Cookbook, Chapter 10, Advanced Mathematics, Drawing commutative diagrams.

Triangle

% Releux triangle
% Author: Stefan Kottwitz
% https://www.packtpub.com/hardware-and-creative/latex-cookbook
\documentclass[border=10pt]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}
  \tkzDefPoint(0,0){A}
  \tkzDefPoint(4,1){B}
  \tkzInterCC(A,B)(B,A)
  \tkzGetPoints{C}{D}
 
  \tkzDrawPolygon(A,B,C)
  \tkzDrawPoints(A,B,C,D)
 
  \tkzLabelPoints[below left](A)
  \tkzLabelPoints(B,D)
  \tkzLabelPoint[above](C){$C$}
 
  \tkzDrawCircle[dotted](A,B)
  \tkzDrawCircle[dotted](B,A)
 
  \tkzCompass[color=red, very thick](A,C)
  \tkzCompass[color=red, very thick](B,C)
 
  \tkzCompass[color=red, very thick](A,D)
  \tkzCompass[color=red, very thick](B,D)
 
  \tkzDrawArc[fill=blue!10,thick](A,B)(C)
    \tkzDrawArc[fill=blue!10,thick](B,C)(A)
    \tkzDrawArc[fill=blue!10,thick](C,A)(B)
 
  \tkzInterLC(A,B)(B,A)
  \tkzGetPoints{F}{E}
  \tkzDrawPoints(E)
  \tkzLabelPoints(E)
  \tkzDrawPolygon(A,E,D)
 
  \tkzMarkAngles[fill=yellow,opacity=0.5](D,A,E A,E,D)
  \tkzMarkRightAngle[size=0.65,fill=red,opacity=0.5](A,D,E)
  \tkzLabelAngle[pos=0.7](D,A,E){$\alpha$}
  \tkzLabelAngle[pos=0.8](A,E,D){$\beta$}
  \tkzLabelAngle[pos=0.5,xshift=-1.4mm](A,D,D){$90^\circ$}
 
  \tkzLabelSegment[below=0.6cm,align=center,font=\small](A,B){Reuleaux\\triangle}
  \tkzLabelSegment[above right,sloped,font=\small](A,E){hypotenuse}
  \tkzLabelSegment[below,sloped,font=\small](D,E){opposite}
  \tkzLabelSegment[below,sloped,font=\small](A,D){adjacent}
  \tkzLabelSegment[below right=4cm,font=\small](A,E){Thales circle}
\end{tikzpicture}
\end{document}
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