Octogone, carré et arctangente
Il suffit de trouver \(\alpha\) en radian et sous forme fractionnaire. \documentclass[border=5mm]{standalone} \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture} \tkzDefPoint(0,0){O} \foreach[count=\i] \ANG in {22.5,67.5,112.5,157.5,202.5,247.5,292.5,337.5} { \tkzDefPoint({5*cos(\ANG*pi/180)},{5*sin(\ANG*pi/180)}){P\i} } \tkzDrawPoints[color=red,fill=white,size=7](P1,P2,P3,P4,P5,P6,P7,P8) \tkzInterLL(P1,P8)(P6,P7) \tkzGetPoint{I} \tkzDefSquare(P1,I) \tkzGetPoints{C}{D} \tkzDrawPolygon[color=black,ultra thick](P1,D,C,I) \tkzDrawPolygon[color=magenta, ultra thick](P7,P8,C) \tkzDrawPolygon[color=red,ultra thick](P1,P2,P3,P4,P5,P6,P7,P8) \tkzMarkAngle[fill=magenta!35,size=2.8cm,opacity=.5](P8,C,P7) \tkzLabelAngle[pos = 2.3](P8,C,P7){\color{black}{\mbox{\Large$\alpha$}}} \end{tikzpicture} \end{document}