TikZ: kartesische oder Polarkoordinaten eines konstruierten Punktes auslesen und weiterverwenden

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\documentclass[margin=5pt, tikz]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[]
\draw[name path=strecke] (0,0) -- (2,2);
\draw[name path=kreis] (1,1) circle[radius=1];
\path[name intersections={of=strecke and kreis, name=S}] ;
\fill[red] (S-1) circle (2pt) node[right]{S};
\draw[] (0,0) circle (2pt);
\path let \p1=(S-1),\n1={veclen(\y1,\x1)},\n2={atan2(\y1,\x1)} in
(S-1) node[right=12pt,text width=4cm]{Mein Radius ist \n1 und mein
Winkel\pgfmathsetmacro{\Winkel}{\n2} % um die pt abzustreifen
\Winkel, also sind meine Polarkoordinaten $(\Winkel:\mbox{\n1})$. Wenn Du Dich
fragst, was das in cm ist: $r=\pgfmathparse{\n1*1pt/1cm}\pgfmathresult\,$cm.  Und
meine  kartesischen Koordinaten sind einfach
$x=\pgfmathparse{\x1*1pt/1cm}\pgfmathresult\,$cm und
$y=\pgfmathparse{\y1*1pt/1cm}\pgfmathresult\,$cm.};
\end{tikzpicture}
\end{document}
 
 
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