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+\documentclass[varwidth=true, border=2pt]{standalone}
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+
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+\usepackage{tkz-euclide}
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+\usetkzobj{all}
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+% Thanks to Jan Hlavacek for giving an example
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+% (http://tex.stackexchange.com/a/16749/5645)
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+
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+\begin{document}
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+\begin{tikzpicture}[scale=3]
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+ \tkzDefPoint(0,0){O}
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+ \tkzDefPoint(1,0){Z}
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+
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+ % Define points
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+ \tkzDefPoint(-0.7,-0.1){A}
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+ \tkzDefPoint(0.4,-0.3){B}
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+ \tkzDefPoint(0.1,0.4){C}
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+
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+ % Draw big circle
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+ \tkzDrawCircle[fill=white](O,Z)
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+
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+ % I have no idea what this does,
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+ % but when I remove it the rest of the image (the big circles)
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+ % get visible. So it seems to crop the image to the size of the circle
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+ \tkzClipCircle(O,Z)
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+
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+ % Draw angles
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+ \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](B,A,C)
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+ \tkzLabelAngle[pos=0.2](B,A,C){$\alpha$}
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+
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+ \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](C,B,A)
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+ \tkzLabelAngle[pos=0.2](C,B,A){$\beta$}
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+
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+ \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](A,C,B)
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+ \tkzLabelAngle[pos=0.2](A,C,B){$\gamma$}
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+
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+
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+ % "Clip" angles
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+ \tkzDrawCircle[fill,orthogonal through=A and B,color=white](O,Z)
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+ \tkzDrawCircle[fill,orthogonal through=A and C,color=white](O,Z)
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+ \tkzDrawCircle[fill,orthogonal through=B and C,color=white](O,Z)
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+
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+ % Draw big circle
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+ \tkzDrawCircle(O,Z)
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+
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+ % Draw lines
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+ \tkzDrawCircle[orthogonal through=A and B,color=green](O,Z)
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+ \tkzDrawCircle[orthogonal through=A and C,color=blue](O,Z)
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+ \tkzDrawCircle[orthogonal through=B and C,color=red](O,Z)
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+
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+ % Draw points and label them
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+ \tkzDrawPoints[color=black,fill=red,size=5](A,B,C)
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+ \tkzLabelPoints(A,B,C)
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+\end{tikzpicture}
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+\end{document}
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