楕円と線の間の領域を塗りつぶすことができません（領域が小さい）

Question

ABC である円弧 (小さい領域) の完全な領域を埋めることができません。円弧の一部が残っています。この点について助けてください。ありがとうございます...

\documentclass{article}
\usepackage{tikz,pgfplots}
%\usepackage[x11names]{xcolor}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usepackage{pgfplots}\pgfplotsset{compat=newest}
\pgfdeclarelayer{bg}    % declare background
\pgfsetlayers{bg,main}  % order of layers (main = standard layer)
\pgfplotsset{compat=1.13}
\usepackage{amsmath}
\usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture} 
\draw (0,-2) -- (0,3); 
\draw (-4,0) -- (5,0);
\draw (0,0)circle[x radius = 3 cm , y radius = 1 cm]; % DRAW ELLIPSE 
\draw (3,0)coordinate[label=below:$A$](a); 
\draw (1,1)coordinate[label=above:$B$](b); 
\draw (0,0)coordinate[label=below left:$O$](o) 
(0,1)coordinate[label=left:$C$](c);
\begin{pgfonlayer}{bg} 
\clip plot (0,0)circle[x radius = 3 cm , y radius = 1 cm];
\fill[blue] (a) -- (b) -- (c) -- (a) -- cycle;
\end{pgfonlayer}
\end{tikzpicture} 
\end{document}

Answer 1

「アーク」というのは、これのことですか？

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\pgfdeclarelayer{bg}    % declare background
\pgfsetlayers{bg,main}  % order of layers (main = standard layer)

\begin{document}
\begin{tikzpicture} 
\draw (0,-2) -- (0,3); 
\draw (-4,0) -- (5,0);
\draw (0,0)circle[x radius = 3 cm , y radius = 1 cm]; % DRAW ELLIPSE 
\draw (3,0)coordinate[label=below:$A$](a); 
\draw (1,1)coordinate[label=above:$B$](b); 
\draw (0,0)coordinate[label=below left:$O$](o) 
(0,1)coordinate[label=left:$C$](c);
\begin{pgfonlayer}{bg} 
\clip plot (0,0)circle[x radius = 3 cm , y radius = 1 cm];
\fill[blue] (a) |- (c) --cycle;
\end{pgfonlayer}
\end{tikzpicture} 
\end{document}