[Tex/LaTex] Tikz-picture – Fill area

tikz-pgf

I'm struggling drawing this picture:

enter image description here

I used

\documentclass[10pt]{article}
\usepackage{ngerman, longtable}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{fancyhdr}
\usepackage{pdflscape}
\usepackage{wasysym}
\usepackage{color}
\usepackage{longtable}
\pagestyle{fancy}
\usepackage{multirow}
\usepackage[pdftex]{graphicx}
\usepackage{array}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=0.6,domain=-3:5]

\path[fill=black,opacity=0.2] (2,0) -- plot[domain=2:0] (0,0) circle (2cm) -- (0,-2) -- cycle;

%draw grid+axis afterwards
\draw[very thin, color=gray,opacity=0.2] (-5.0,-5.0) grid (5.0,5.0);
\draw[->,color=black] (-5.5,0) -- (5.5,0);
\foreach \x in {-5,-4,-3,-2,-1,1,2,3,4,5}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-5.5) -- (0,5.5);
\draw (5.7,0.2) node[anchor=north west] {$x_1$};
\draw (-0.3,6.2) node[anchor=north west] {$x_2$};
\foreach \y in {-5,-4,-3,-2,-1,1,2,3,4,5}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};

%draw cirle + graph
\draw[color=black] plot (\x,{(\x-2)}) node[right] {};
\draw (0,0) circle (2cm);

\end{tikzpicture}
\end{document}

I get a circle and a line, but the circle is completely filled and I thought 

\path[fill=black,opacity=0.2] (2,0) -- plot[domain=2:0] (0,0) circle (2cm) -- (0,-2) -- cycle;

removes the intended area. Perhaps someone can help me out?

Best Answer

Another way, especially in more complex cases in which you are not sure about angles, is to just put \path [clip] (-3,-5)--(5,3)--(-3,3)--cycle; in a new scope together with your statement (without any change) \path[fill=black,opacity=0.2] (2,0) -- plot[domain=2:0] (0,0) circle (2cm) -- (0,-2) -- cycle; as follows:

\documentclass[10pt]{article}
\usepackage{ngerman, longtable}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{fancyhdr}
\usepackage{pdflscape}
\usepackage{wasysym}
\usepackage{color}
\usepackage{longtable}
\pagestyle{fancy}
\usepackage{multirow}
\usepackage[pdftex]{graphicx}
\usepackage{array}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=0.6,domain=-3:5]

\begin{scope}
\path [clip] (-3,-5)--(5,3)--(-3,3)--cycle;
\path[fill=black,opacity=0.2] (2,0) -- plot[domain=2:0] (0,0) circle (2cm) -- (0,-2) -- cycle;
\end{scope}

%draw grid+axis afterwards
\draw[very thin, color=gray,opacity=0.2] (-5.0,-5.0) grid (5.0,5.0);
\draw[->,color=black] (-5.5,0) -- (5.5,0);
\foreach \x in {-5,-4,-3,-2,-1,1,2,3,4,5}
\draw[shift={(\x,0)},color=black] (0pt,2pt) -- (0pt,-2pt) node[below] {\footnotesize $\x$};
\draw[->,color=black] (0,-5.5) -- (0,5.5);
\draw (5.7,0.2) node[anchor=north west] {$x_1$};
\draw (-0.3,6.2) node[anchor=north west] {$x_2$};
\foreach \y in {-5,-4,-3,-2,-1,1,2,3,4,5}
\draw[shift={(0,\y)},color=black] (2pt,0pt) -- (-2pt,0pt) node[left] {\footnotesize $\y$};
\draw[color=black] (0pt,-10pt) node[right] {\footnotesize $0$};

%draw cirle + graph
\draw[color=black] plot (\x,{(\x-2)}) node[right] {};
\draw (0,0) circle (2cm);

\end{tikzpicture}
\end{document}

which gives the required picture:

enter image description here

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