add tag
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

![ScreenHunter 70.png](/image?hash=aace387b3d017a260ea7e4b782a2ad46772c643e6740989d38aa2f08e0e0e85b)

Top Answer
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.
\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];
  	pic{3d/circle on sphere={R=R,C={(I)},P={(O)}}};
![Screen Shot 2021-04-01 at 7.36.33 PM.png](/image?hash=a1717d8279ca86cf29f749297c5f126d59e06bf06357aa4d9e013fbd3f2dcce5)

Enter question or answer id or url (and optionally further answer ids/urls from the same question) from

Separate each id/url with a space. No need to list your own answers; they will be imported automatically.