# Example: Lune of Hippocrates

Published 2008-11-27 | Author: Alain Matthes

What is the relationship between the area of the isosceles right triangle ABC and the area of the lune?

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% 25/11/2008
% Alain Matthes
\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{through,calc}
\begin{document}

\begin{tikzpicture}[thick]
\path[draw] (-4,0)  coordinate [label= left:$A$] (A)
-- ( 0,4)  coordinate [label=above:$C$] (C)
-- ( 4,0)  coordinate [label=right:$B$] (B)
-- cycle;
\foreach \point in {A,B,C}
\fill [black] (\point) circle (2pt);
\draw [color=red] circle(4cm);
% The radius of the inner circular arc is equal to the length of BC.
% Use the math engine to do the necessary calculations and store the
% radius in the \n1 register
\draw[color=red,fill=black!20]
let \p1 = ($(B) - (C)$),
\n1 = {veclen(\x1,\y1)} in
(A) arc (180:360:4cm) arc (-45:-135:\n1);
\end{tikzpicture}
\end{document}