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\documentclass[border=1.5mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tkz-euclide,amsmath}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}[line join=round]
\def\a{3}
\tkzDefPoint(0,0){A}
\tkzDefPoint(\a,0){B}
\tkzDefPoint(\a,\a){C}
\tkzDefPoint(0,\a){D}
\tkzDefPoint(\a/2,\a/2){O}
\tkzDrawPolygon[thick](A,B,C,D)
\tkzDefMidPoint(A,B)\tkzGetPoint{M}
\tkzDefPointsBy[rotation=center O angle 90](M,N,P){N,P,Q}
\tkzDrawSegments[thick](A,N B,P C,Q D,M)
\tkzInterLL(A,N)(D,M)
\tkzGetPoint{E}
\tkzDefPointsBy[rotation=center O angle 90](E,F,G){F,G,H}
\foreach \point/\position in {A/below,B/below,M/below,E/below,N/right,F/right,
G/right,P/above,C/above,Q/left,H/left,D/above}
{\fill[](\point) circle (1.5 pt);
\node[\position=2pt] at (\point) {$\point$};
}
\end{tikzpicture}
\end{document}