This image is pretty close to what I want to make (a simple hyperbolic triangle with marked angles):

enter image description here

However, as you can see, the angles are not marked correctly. How can I mark them? Can I mark the exterior angles the same way?

MWE

\documentclass[varwidth=true, border=2pt]{standalone}

\usepackage{tkz-euclide}
\usetkzobj{all}
% Thanks to Jan Hlavacek for giving an example
% (http://tex.stackexchange.com/a/16749/5645)

\begin{document}
\begin{tikzpicture}[scale=3]
    \tkzDefPoint(0,0){O}
    \tkzDefPoint(1,0){Z}

    \tkzDrawCircle(O,Z)

    % Define points
    \tkzDefPoint(-0.7,-0.1){A}
    \tkzDefPoint(0.4,-0.3){B}
    \tkzDefPoint(0.1,0.4){C}

    % I have no idea what this does,
    % but when I remove it the rest of the image (the big circles)
    % get visible. So it seems to crop the image to the size of the circle
    \tkzClipCircle(O,Z)

    % Draw lines
    \tkzDrawCircle[orthogonal through=A and B,color=green](O,Z)
    \tkzDrawCircle[orthogonal through=A and C,color=blue](O,Z)
    \tkzDrawCircle[orthogonal through=B and C,color=red](O,Z)

    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](B,A,C)
    \tkzLabelAngle[pos=0.2](B,A,C){$\alpha$}

    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](C,B,A)
    \tkzLabelAngle[pos=0.2](C,B,A){$\beta$}

    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](A,C,B)
    \tkzLabelAngle[pos=0.2](A,C,B){$\gamma$}

    % Draw points and label them
    \tkzDrawPoints[color=black,fill=red,size=12](A,B,C)
    \tkzLabelPoints(A,B,C)
\end{tikzpicture}
\end{document}

You can do this by first marking the angles, then "clipping" them by covering them with white, and finally drawing the rest of the picture. It's a bit of a hack and might not work in every case, but it works here.

Angles in a hyperbolic triangle

\documentclass[varwidth=true, border=2pt]{standalone}

\usepackage{tkz-euclide}
\usetkzobj{all}
% Thanks to Jan Hlavacek for giving an example
% (http://tex.stackexchange.com/a/16749/5645)

\begin{document}
\begin{tikzpicture}[scale=3]
    \tkzDefPoint(0,0){O}
    \tkzDefPoint(1,0){Z}

    % Define points
    \tkzDefPoint(-0.7,-0.1){A}
    \tkzDefPoint(0.4,-0.3){B}
    \tkzDefPoint(0.1,0.4){C}

    % I have no idea what this does,
    % but when I remove it the rest of the image (the big circles)
    % get visible. So it seems to crop the image to the size of the circle
    \tkzClipCircle(O,Z)

    % Draw angles
    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](B,A,C)
    \tkzLabelAngle[pos=0.2](B,A,C){$\alpha$}

    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](C,B,A)
    \tkzLabelAngle[pos=0.2](C,B,A){$\beta$}

    \tkzMarkAngles[fill= orange,size=0.3cm,opacity=.3](A,C,B)
    \tkzLabelAngle[pos=0.2](A,C,B){$\gamma$}

    % "Clip" angles
    \tkzDrawCircle[fill,orthogonal through=A and B,color=white](O,Z)
    \tkzDrawCircle[fill,orthogonal through=A and C,color=white](O,Z)
    \tkzDrawCircle[fill,orthogonal through=B and C,color=white](O,Z)

    % Draw big circle
    \tkzDrawCircle(O,Z)

    % Draw lines
    \tkzDrawCircle[orthogonal through=A and B,color=green](O,Z)
    \tkzDrawCircle[orthogonal through=A and C,color=blue](O,Z)
    \tkzDrawCircle[orthogonal through=B and C,color=red](O,Z)

    % Draw points and label them
    \tkzDrawPoints[color=black,fill=red,size=12](A,B,C)
    \tkzLabelPoints(A,B,C)
\end{tikzpicture}
\end{document}
  • Although this works for interior angles (+1) it seems not to work for exterior angles. – Martin Thoma Oct 4 '14 at 8:03
  • That seems to be harder since '\tkzClipCircle' doesn't seem to work with '[orthogonal through=...]' (but I might have missed something in the French documentation). My guess is that you would have to use some geometry to find the centers of the three circles and use that (in combination with the technique for interior angles) to do the exterior. (For example drawing a big angle around C, clip it inside the blue circle and cover the part inside the red circle.) Positioning the labels could also be a bit tricky, but it should work with some manual tweaking. – Jonas Granholm Oct 4 '14 at 11:30

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