Fill area of circle delimited by a segment I want to fill the area delimited by the horizontal line and the bottom part of the circle blue. I followed the answers given in this post shade the segment of a circle but somehow my code fills exactly the complement of the circle.
Here is my MWE
\documentclass[hidelinks,12pt,twoside,a4paper,reqno]{amsbook}
\usepackage{tikz}
\begin{document}
\begin{figure}[!h]
\centering
\begin{tikzpicture}
\coordinate (C) at (0,0);
\coordinate (A) at (200:pi);
\coordinate (B) at (-20:pi);
\fill[blue!40] (A) arc[start angle=200, end angle=-20, radius=pi] -- cycle;
\draw (C) -- (A);
\draw (C) -- (B);
\draw (A) -- (B);
\draw (0,0) node[circle,draw,inner sep=1pt](C) {} circle (pi);
\end{tikzpicture}
\end{figure}
\end{document}


Can please somebody tell me what I am missing? If I understood correctly, changing the start and end angle of the arc command should give the result but that just messes it up completely.

Like this?

\documentclass[hidelinks,12pt,twoside,a4paper,reqno]{amsbook}
\usepackage{tikz}
\begin{document}
\begin{figure}[!h]
\centering
\begin{tikzpicture}
\coordinate (C) at (0,0);
\coordinate (A) at (200:pi);
\coordinate (B) at (-20:pi);
\fill[blue!40] (A) arc[start angle=200, end angle=340, radius=pi];
\draw (A) -- (B) -- (C) -- cycle;
\draw (0,0) node[circle,draw,inner sep=1pt]{} (C) circle (pi);
\end{tikzpicture}
\end{figure}
\end{document}


With a path picture you can draw whatever you want inside a path and the result is clipped by the path. In this case, a rectangle large enough is clipped by the lower part of the circle.
\documentclass[hidelinks,12pt,twoside,a4paper,reqno]{amsbook}
\usepackage{tikz}
\begin{document}
\begin{figure}[!h]
\centering
\begin{tikzpicture}
\coordinate (C) at (0,0);
\coordinate (A) at (200:pi);
\coordinate (B) at (-20:pi);
\draw (C) -- (A); 
\draw (C) -- (B);
\draw (A) -- (B);
\draw[path picture={ \draw[fill=blue!30] (200:pi) rectangle ++(7,-3);}] (0,0)   
node[circle,draw,inner sep=1pt](C) {} circle (pi);
\end{tikzpicture}
\end{figure}
\end{document}