Anonymous 1123
From the internet, I can find many figures  about a cone inscribed a sphere. This is one of them.

![ScreenHunter 69.png](/image?hash=3809fd9b3b505fdbcd5885d6279f5aa353e046a437fd72012653f9f5692607a1)

Is the above figure correct?

I use GeospacW to draw a cone inscribed a sphere with radius R and AB is diameter of the cone. I get


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);