General ⇒ How can I draw a cylinder that inscribes a sphere?

[Tran Van Toan]

I am trying to draw this picture in Tikz. I tried.

Code: Select all

\documentclass[12pt,border=3mm]{standalone}
\usepackage{fouriernc}
\usepackage{tikz}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc,backgrounds}
\begin{document}
\tdplotsetmaincoords{60}{110}
\def\r{{2*sqrt(3)}}
\begin{tikzpicture}
[scale=1,tdplot_main_coords]
\path
coordinate (O) at (0,0,0)
coordinate (T) at  (0,0,2)
coordinate (A') at  (0,\r,4)
coordinate (A) at  (0,\r,0);
\coordinate (B) at ($(O) + (-50:{2*sqrt(3)} and \r)$);
\coordinate (B') at ($(B)+(0,0,4)$);
\coordinate (O') at ($(O)+(0,0,4)$);
\draw[dashed] (A)--(A') (B) --(B') (O)--(O') (O)--(A) (T) --(A);
\foreach \v/\position in {T/above,O/below,O'/above,A/below,B/below,A'/left,B'/left} {
    \draw[draw =black, fill=black] (\v) circle (1.2pt) node [\position=0.2mm] {$\v$};
}
\begin{scope}[tdplot_screen_coords, on background layer]
\pgfmathsetmacro{\R}{4}%
%\pgfmathsetmacro{\r}{{2*sqrt(3)}}%
\fill[ball color=cyan!50, opacity=1.0] (T) circle (\R);
\end{scope}
\tkzMarkRightAngle[size = 0.3](T,O,A);
\draw [thick] (B) arc (-50:90:\r);
\draw [thick, dashed] (A) arc (90:310:\r);
\draw [thick] (B') arc (-50:90:\r);
\draw [thick, dashed] (A') arc (90:310:\r);
\end{tikzpicture}
\end{document}

The cylinder look very bad. How can I repair?