Gfyuki

I have a sphere (taken from http://www.texample.net/tikz/examples/, credits to Bartman):

    % Steradian cone in sphere

% Author: Bartman

documentclass[tikz,border=10pt]{standalone}

%%%<

usepackage{verbatim}

%%%>

begin{comment}

:Title: Steradian cone in sphere

:Tags: 3D;Angles;Intersections;Shadings;MMathematics;Geometry

:Author: Bartman

:Slug: steradian-cone-sphere



A graphical representation of a steradian.

It is the solid angle subtended at the center

of a unit sphere by a unit area on its surface. (Wikipedia)



Made by Bartman on

http://golatex.de/3d-kugel-in-tikz-t17380.html



The part of the cone is from http://tex.stackexchange.com/a/186109/213

end{comment}

usepackage{sansmath}

usetikzlibrary{shadings,intersections}

begin{document}

begin{tikzpicture}[font = sansmath]

  coordinate (O) at (0,0);







  % ball background color

  shade[ball color = blue, opacity = 0.2] (0,0) circle [radius = 2cm];



  % cone

  begin{scope}

    defrx{0.71}% horizontal radius of the ellipse

    defry{0.15}% vertical radius of the ellipse

    defz{0.725}% distance from center of ellipse to origin



    path [name path = ellipse]    (0,z) ellipse ({rx} and {ry});

    path [name path = horizontal] (-rx,z-ry*ry/z)

                                -- (rx,z-ry*ry/z);

    path [name intersections = {of = ellipse and horizontal}];





  end{scope}





  % ball

  draw (O) circle [radius=2cm];

  % label of ball center point

  filldraw (O) circle (1pt) node[below] {$O$};



  % radius

  draw[densely dashed] (O) to [edge label = $1$] (-1.33,1.33);

  draw[densely dashed] (O) -- (1.33,1.33);



  % cut of ball surface

  draw[red, densely dashed] (-1.36,1.46) arc [start angle = 170, end angle = 10,

    x radius = 13.8mm, y radius = 3.6mm];

  draw[red] (-1.29,1.52) arc [start angle=-200, end angle = 20,

    x radius = 13.75mm, y radius = 3.15mm];



  % label of cut of ball surface

  draw (-1.2,2.2) -- (-0.23,1.1) node at (-1.37,2.37) {$B$};

end{tikzpicture}

end{document}

I want to add an angle alpha like this:

How can I do this?

First, you have to name the coordinate for the edges of the angle. Here I use (x) and (y).

documentclass[tikz,border=10pt]{standalone}

usepackage{sansmath}

usetikzlibrary{shadings,intersections,quotes,angles}

begin{document}

begin{tikzpicture}[font = sansmath]

  coordinate (O) at (0,0);

  shade[ball color = blue, opacity = 0.2] (0,0) circle [radius = 2cm];

  begin{scope}

    defrx{0.71}% horizontal radius of the ellipse

    defry{0.15}% vertical radius of the ellipse

    defz{0.725}% distance from center of ellipse to origin

    path [name path = ellipse]    (0,z) ellipse ({rx} and {ry});

    path [name path = horizontal] (-rx,z-ry*ry/z)

                                -- (rx,z-ry*ry/z);

    path [name intersections = {of = ellipse and horizontal}];

  end{scope}

  draw (O) circle [radius=2cm];

  filldraw (O) circle (1pt) node[below] {$O$};

  draw[densely dashed] (O) to [edge label = $1$] (-1.33,1.33) coordinate (x);

  draw[densely dashed] (O) -- (1.33,1.33) coordinate (y);

  draw[red, densely dashed] (-1.36,1.46) arc [start angle = 170, end angle = 10,

    x radius = 13.8mm, y radius = 3.6mm];

  draw[red] (-1.29,1.52) arc [start angle=-200, end angle = 20,

    x radius = 13.75mm, y radius = 3.15mm];

  draw (-1.2,2.2) -- (-0.23,1.1) node at (-1.37,2.37) {$B$};



  % Command for the angle

  pic[draw,->,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"] {angle=y--O--x};

end{tikzpicture}

end{document}

This is just a small addendum to Joule V's nice answer, which solved the main problem. By now there are IMHO much better tools available to draw such graphs.

1. 
   tikz-3dplot allows you to install orthographic projections, i.e. dial the view angles.


2. The 3d library allows you to switch to a plane to e.g. draw a latitude circle. So you no longer need to guess ellipses.


3. The angle of visibility, i.e. the angle at which the dashed lines turn in solid ones and vice versa has been compute e.g. here, so you do not need to guess this either.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,backgrounds,quotes,angles}

begin{document}

tdplotsetmaincoords{80}{00}

begin{tikzpicture}[tdplot_main_coords]

 pgfmathsetmacro{R}{2} % radius

 pgfmathsetmacro{myang}{50} % latitude angle of the red circle

 coordinate (O) at (0,0,0);

 shade[ball color = blue, opacity = 0.2,tdplot_screen_coords] 

 (O) circle [radius = R*1cm];

 begin{scope}[canvas is xy plane at z={R*sin(myang)},transform shape]

  % angVis from https://tex.stackexchange.com/a/49589/121799

  pgfmathsetmacroangVis{atan(sin(myang)*cos(tdplotmaintheta)/sin(tdplotmaintheta))}

  begin{scope}[on background layer]

   draw[red,dashed] (angVis:{R*cos(myang)}) arc (angVis:180-angVis:{R*cos(myang)});

  end{scope}  

  draw[red] (180-angVis:{R*cos(myang)}) arc (180-angVis:360+angVis:{R*cos(myang)});

  path (0:{R*cos(myang)}) coordinate (R) 

  (180:{R*cos(myang)}) coordinate (L);

 end{scope}

 begin{scope}[on background layer]

  draw[dashed] (L) -- (O) node[midway,below] {$L$} -- (R);

  fill (O) circle[radius=1pt] node[below] {$O$};

  pic[draw,-latex,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"] 

  {angle=R--O--L};

 end{scope} 

end{tikzpicture}

end{document}

The following animation shows that you can dial view and latitude as you wish.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{3d,backgrounds,quotes,angles}

begin{document}

foreach Angle in {5,15,...,355}

{tdplotsetmaincoords{70+cos(Angle)}{00}

begin{tikzpicture}[tdplot_main_coords]

 pgfmathsetmacro{R}{2} % radius

 pgfmathsetmacro{myang}{40+15*sin(2*Angle)} % latitude angle of the red circle

 coordinate (O) at (0,0,0);

 shade[ball color = blue, opacity = 0.2,tdplot_screen_coords] 

 (O) circle [radius = R*1cm];

 begin{scope}[canvas is xy plane at z={R*sin(myang)},transform shape]

  % angVis from https://tex.stackexchange.com/a/49589/121799

  pgfmathsetmacroangVis{atan(sin(myang)*cos(tdplotmaintheta)/sin(tdplotmaintheta))}

  begin{scope}[on background layer]

   draw[red,dashed] (angVis:{R*cos(myang)}) arc (angVis:180-angVis:{R*cos(myang)});

  end{scope}  

  draw[red] (180-angVis:{R*cos(myang)}) arc (180-angVis:360+angVis:{R*cos(myang)});

  path (0:{R*cos(myang)}) coordinate (R) 

  (180:{R*cos(myang)}) coordinate (L);

 end{scope}

 begin{scope}[on background layer]

  draw[dashed] (L) -- (O) node[midway,below] {$L$} -- (R);

  fill (O) circle[radius=1pt] node[below] {$O$};

  pic[draw,-latex,angle radius=.5cm,angle eccentricity=1.3,"$alpha$"] 

  {angle=R--O--L};

 end{scope} 

end{tikzpicture}}

end{document}