Is this a correct figure about a cone inscribed a sphere? - TeX

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user 3.14159

I believe GeoSpace is correct, at least under usual assumptions that make orthographic projections a good approximation. I further believe that the picture from the internet is not entirely correct.

Here is what I get with `3dtools`. It more or less coincides with the GeoSpace result.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[3d/install view={phi=60,theta=70},
	line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt},
	declare function={R=4;r=R*0.8;h=R+sqrt(R*R-r*r);}] 
  \path (0,0,0) coordinate[c,label=below:{$I$}] (I)	
  	 (0,0,R-h) coordinate[c,label=below:{$O$}] (O) 
	 (0,0,R) coordinate[c,label=above:{$N$}] (N) 
	 (0,0,-R) coordinate[c,label=below:{$S$}] (S);
  \path[3d/visible/.style={draw,very thin,cheating dash}]
		(O) pic{3d/cone={r=r,h=h}}
		(N) edge[3d/hidden] (S);
  \draw[3d/screen coords] (I) circle[radius=R];
  \path[3d/hidden/.style={draw=none}] 
  	pic{3d/circle on sphere={R=R,C={(I)},P={(O)}}};
\end{tikzpicture}
\end{document} 
```
![Screen Shot 2021-04-01 at 7.36.33 PM.png](/image?hash=a1717d8279ca86cf29f749297c5f126d59e06bf06357aa4d9e013fbd3f2dcce5)

The result looks correct. You could also use ``` \documentclass[tikz,border=1cm]{standalone} \usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {0,5,...,360} {\begin{tikzpicture}[font=\footnotesize, line join=round, line cap=round,3d/install view={phi=20,theta=70}, declare function={R=4;h=6;r=sqrt(R*R-(h-R)*(h-R));}] \path[3d/visible/.style={draw,very thin,cheating dash}] (0,0,0) coordinate (O) (0,0,R-h) coordinate(P) pic{3d/cone={r=r,h=h}}; \path pic[3d/hidden/.style={draw=none}]{3d/circle on sphere={R=R,P={(P)}}} pic{3d/circle on sphere={R=R,P={(O)},n={(0,0,1)}}} pic{3d/circle on sphere={R=R,P={(O)},n={(1,0,0)}}}; \draw[3d/screen coords] (O) circle[radius=R]; \path[shift={(P)}] (\Angle:r) coordinate (m); \draw[3d/hidden] (m) -- (0,0,R); \end{tikzpicture}} \end{document} ```

@marmot, re: [your answer](#a1942), Is this code correct? ``` \documentclass[tikz,border=1cm]{standalone} \usetikzlibrary{calc,intersections} \begin{document} \foreach \i in{0,5,...,360}{ \begin{tikzpicture}[font=\footnotesize, line join=round, line cap=round, >=stealth] \def\x{80} \def\a{4}\def\b{0.3*\a} \def\t{-10} \pgfmathsetmacro{\m}{\b/(sin(\t)} \pgfmathsetmacro{\n}{-(\b*sin(\t)-(\a*cos(\t))^2/(\b*sin(\t)-\m)} \pgfmathsetmacro{\l}{sqrt((\a*cos(\t))^2+(\n-\b*sin(\t))^2)} \pgfmathsetmacro{\h}{\n+\l-0.5*\b}% heigh \pgfmathsetmacro{\s}{asin(\b/\h)} \path({\a*cos(\t)},{\b*sin(\t)})coordinate(A)(0,\n)coordinate(I); \clip(I) circle(\l+0.45); \draw let \p1=($(A)-(I)$) in (I) circle ({veclen(\x1,\y1)}); \coordinate (N) at ({\a*cos(\s)}, {\b*sin(\s)}); \coordinate(M) at ({-\a*cos(\s)}, {\b*sin(\s)}); \path(0,\h)coordinate(A)(0,0)coordinate(H)(0,\n)coordinate(I)(\a,0)arc(0:{\i}:{\a} and {\b})coordinate(m); \draw(\t: {\a} and {\b})arc(\t:{-180-\t}:{\a} and {\b}); \path[name path =oy]([shift={(-90:\l)}]I)--(I)--++(90:\l); \draw[name path=elipmot,dotted,rotate around={\x:(I)}](\l,\n)arc(0:-180:{\l} and {0.3*\l}); \draw[name path=eliphai,rotate around={\x:(I)}](\l,\n)arc(0:180:{\l} and {0.3*\l}); \path[name intersections ={ of = oy and elipmot,by={B}}]; \path[name intersections ={ of = oy and eliphai,by={A}}]; \draw[dotted](\t: {\a} and {\b})arc(\t:{180-\t}:{\a} and {\b})(N)--(A)--(B)(H)--(N)(\l,\n)arc(0:180:{\l} and {0.3*\l})(A)--(M)--(H)(I)--++(180:\l)(I)--++(0:\l)(m)--(A); \foreach \d/\g in{B/-90,A/90,M/120,I/40,H/-135,m/190} \draw[fill=black](\d)circle(1pt)node[shift={(\g:0.35)}]{$\d$}; \draw (\l,\n)arc(0:-180:{\l} and {0.35*\l}); \end{tikzpicture} } \end{document} ```

Yes, of course. For instance by switching on the `psi` angle. ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \begin{tikzpicture}[3d/install view={phi=60,theta=70,psi=40}, line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt}, declare function={R=4;r=R*0.8;h=R+sqrt(R*R-r*r);}] \path (0,0,0) coordinate[c,label=below:{$I$}] (I) (0,0,R-h) coordinate[c,label=below:{$O$}] (O) (0,0,R) coordinate[c,label=above:{$N$}] (N) (0,0,-R) coordinate[c,label=below:{$S$}] (S); \path[3d/visible/.style={draw,very thin,cheating dash}] (O) pic{3d/cone={r=r,h=h}} (N) edge[3d/hidden] (S); \draw[3d/screen coords] (I) circle[radius=R]; \path[3d/hidden/.style={draw=none}] pic{3d/circle on sphere={R=R,C={(I)},P={(O)}}}; \end{tikzpicture} \end{document} ``` ![Screen Shot 2021-04-01 at 9.36.15 PM.png](/image?hash=101bba1f94dc34ba39ac56e8ab177a6f4a96bae0efb32727a119c6b9859a29b9)

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