Quadrate über Radien und weitere Konstruktionslinien in Inkreis eines Quadrats einzeichnen

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\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{through}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[
  scale=.1,
  dot/.style = {
    draw,fill,inner sep=1pt,
    label={#1}
  }]
  \path% mehrmals genutzte Punkte als coordinate speichern
    (29,29) coordinate (M)
    (9,8) coordinate (P)
    (P-|M) coordinate (H)% Schnittpunkt Horizontale durch P und Vertikale durch M
  ;
  \node[dot={below:$(5|5)$}] at (5,5) {};
  \node[dot={{[label distance=7pt]above:$(9|8)$}}] at (P) {};
  \node[dot={above right:$(29|29)$}] at (M) {};
  \node[draw,circle through={(P)}] (c) at (M) {};
  \draw[help lines] (c.west |- c.north) rectangle (c.east |- c.south);
  \draw (c.west |- P) -- (P) -- (c.south -| P);
  \draw (H)--(P)--(M)--(c.south);
  \draw [dashed]% Quadrate über Linien
    (P)--($(P)!1!90:(M)$)--($(M)!1!-90:(P)$)coordinate(hpm)--(M)
    (M)--($(M)!1!90:(H)$)--($(H)!1!-90:(M)$)coordinate(hmh)--(H)
    (c.south)--($(H)!1!90:(P)$)--($(P)!1!-90:(H)$)coordinate(hhp)--(P|-c.south)
  ;
  \path% Beschriftung der Quadrate
    (P) -- node {$r^2$}(hpm)
    (M) -- node {$(r-8)^2$}(hmh)
    (H) -- node [below] {$(r-9)^2$}(hhp)
  ;
\end{tikzpicture}
\end{document}
 
 
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