TikZ: Wie kann ich durch 'calc' vorgegebene Größen für weitere Berechnung verwenden?

\documentclass[margin=5mm, tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usetikzlibrary{patterns}
\usetikzlibrary{calc}

\pgfmathsetmacro{\Radius}{3}
\pgfmathsetmacro{\bH}{2}
\begin{document}
\begin{tikzpicture}[every node/.style={black,above right}]

\path[name path=line 2] (-1.1*\Radius,-\bH) -- (1.1*\Radius,-\bH);
\path[name path=line 1] (-1.1*\Radius,\bH)  -- (1.1*\Radius,\bH);

\draw[name path=Circle] (0,0) circle[radius=\Radius];
\fill[] (0,0) circle[radius=2pt];

\fill[red,name intersections={of=line 1 and Circle,total=\t}]
    \foreach \s in {1,...,\t}{(intersection-\s) circle (2pt) node {}};
\path[red] (intersection-1) coordinate (C) -- (intersection-2) coordinate (D) ;

\fill[red,name intersections={of=line 2 and Circle,total=\t}]
\foreach \s in {1,...,\t}{
(intersection-\s) circle (2pt) node (P-\s) {}};
\path[red] (intersection-1) coordinate (A) -- (intersection-2) coordinate (B) ;

\draw[red, pattern=north west lines, pattern color=red] (A) rectangle (C);

% Berechnungen
\path (A) let   \p1 = ($ (B) - (A) $),  \n1 = {veclen(\x1,\y1)} 
    in -- (B) node[draw, yshift=-1cm]  {AB :\n1};
%\pgfmathsetmacro{\Laenge}{\n1} % Geht nicht!

\path (B) let   \p1 = ($ (C) - (B) $),  \n1 = {veclen(\x1,\y1)} 
    in --  (B) node[draw]  {BC :\n1};
%\pgfmathsetmacro{\Breite}{\n1}

\pgfmathsetmacro{\Flaeche}{\Laenge*\Breite}
\node[red] at (0,4) {Fl\"ache=?};

\end{tikzpicture}

\end{document}