Anonymous 1123
I am trying to draw  the circle passing through three points A,O,O' and three points A, C, C'. I tried

\documentclass[12pt]{standalone}
\usepackage{tikz-3dplot-circleofsphere}
\usetikzlibrary{3dtools}
\begin{document}
\tdplotsetmaincoords{70}{150}
\begin{tikzpicture}[scale=1,tdplot_main_coords,declare function={a=3;R=a*sqrt(2);r=a;Angle=acos(r/R);
}]
\path (0,0,0) coordinate (C)
({a*sqrt(3)},0,0) coordinate (B)
({a*sqrt(3)/2},a/2,0) coordinate (A)
({a*sqrt(3)/2},-a/2,0) coordinate (O)
(0,0,2*a) coordinate (C')
({a*sqrt(3)},0,2*a) coordinate (B')
({a*sqrt(3)/2},a/2,2*a) coordinate (A')
({a*sqrt(3)/2},-a/2,2*a) coordinate (O')
({a*sqrt(3)/2},-a/2,a) coordinate (I)
;
\foreach \p in {A,B,C,O,A',B',C',O',I}
\draw[fill=black] (\p) circle (1.5 pt);
\foreach \p/\g in {A/90,B/90,C/90,O/90,A'/90,B'/90,C'/90,O'/90,I/60}
\path (\p)+(\g:3mm) node{$\p$};
\foreach \X in {A,B,C,O} \draw[dashed]  (\X) -- (\X');
\draw[dashed]  (A) --(B)  -- (O) -- (C) -- cycle
(A') --(B')  -- (O') -- (C') -- cycle (O) -- (A) (O') -- (A')
;
\begin{scope}[tdplot_screen_coords]
\draw[thick] (I) circle (R);
\end{scope}
\begin{scope}[shift={(I)}]
\tdplotCsDrawLatCircle[tdplotCsFront/.style={thick}]{R}{{-Angle}}
\tdplotCsDrawLatCircle[tdplotCsFront/.style={thick,blue}]{R}{{Angle}}
\end{scope}
\pic[draw=none,dashed]{3d circle through 3 points={A={(A)},B={(C)},C={(C')}}};
\begin{scope}[shift={(I)}]
\path[overlay] [3d coordinate={(A-C)=(A)-(C)},
3d coordinate={(A-C')=(A)-(C')},
3d coordinate={(myn)=(A-C)x(A-C')},
3d coordinate={(A-M)=(A)-(M)}];
\pgfmathsetmacro{\myaxisangles}{axisangles("(myn)")}
\pgfmathsetmacro{\myalpha}{{\myaxisangles}[0]}
\pgfmathsetmacro{\mybeta}{{\myaxisangles}[1]}
\pgfmathsetmacro{\mygamma}{acos(sqrt(TD("(A-M)o(A-M)"))/R)}
\tdplotCsDrawCircle[tdplotCsFront/.style={thick}]{R}{\myalpha}{\mybeta}{\mygamma}
\end{scope}
\end{tikzpicture}
\tdplotsetmaincoords{70}{150}
\begin{tikzpicture}[scale=1,tdplot_main_coords,declare function={a=3;R=a*sqrt(2);r=a;Angle=acos(r/R);
}]
\path (0,0,0) coordinate (C)
({a*sqrt(3)},0,0) coordinate (B)
({a*sqrt(3)/2},a/2,0) coordinate (A)
({a*sqrt(3)/2},-a/2,0) coordinate (O)
(0,0,2*a) coordinate (C')
({a*sqrt(3)},0,2*a) coordinate (B')
({a*sqrt(3)/2},a/2,2*a) coordinate (A')
({a*sqrt(3)/2},-a/2,2*a) coordinate (O')
({a*sqrt(3)/2},-a/2,a) coordinate (I)
;
\foreach \p in {A,B,C,O,A',B',C',O',I}
\draw[fill=black] (\p) circle (1.5 pt);
\foreach \p/\g in {A/90,B/90,C/90,O/90,A'/90,B'/90,C'/90,O'/90,I/60}
\path (\p)+(\g:3mm) node{$\p$};
\foreach \X in {A,B,C,O} \draw[dashed]  (\X) -- (\X');
\draw[dashed]  (A) --(B)  -- (O) -- (C) -- cycle
(A') --(B')  -- (O') -- (C') -- cycle (O) -- (A) (O') -- (A')
;
\begin{scope}[tdplot_screen_coords]
\draw[thick] (I) circle (R);
\end{scope}
\begin{scope}[shift={(I)}]
\tdplotCsDrawLatCircle[tdplotCsFront/.style={thick}]{R}{{-Angle}}
\tdplotCsDrawLatCircle[tdplotCsFront/.style={thick,blue}]{R}{{Angle}}
\end{scope}
\pic[draw=none,dashed]{3d circle through 3 points={A={(A)},B={(O)},C={(O')}}};
\begin{scope}[shift={(I)}]
\path[overlay] [3d coordinate={(A-O)=(A)-(O)},
3d coordinate={(A-O')=(A)-(O')},
3d coordinate={(myn)=(A-O)x(A-O')},
3d coordinate={(A-M)=(A)-(M)}];
\pgfmathsetmacro{\myaxisangles}{axisangles("(myn)")}
\pgfmathsetmacro{\myalpha}{{\myaxisangles}[0]}
\pgfmathsetmacro{\mybeta}{{\myaxisangles}[1]}
\pgfmathsetmacro{\mygamma}{acos(sqrt(TD("(A-M)o(A-M)"))/R)}
\tdplotCsDrawCircle[tdplotCsFront/.style={thick}]{R}{\myalpha}{\mybeta}{\mygamma}
\end{scope}
\end{tikzpicture}
\end{document}


![ScreenHunter 775.png](/image?hash=570dfcef54959986dd46bef5c75879bdfa2d74b9ebed9c2ef90f91e6ba4e498a)

The circle A,C,C' correct and the circle A, O, O' incorrect. Where is wrong in above code?

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