\documentclass[border=1mm,12pt,tikz]{standalone}
\usetikzlibrary{3dtools,calc}
\begin{document}
\foreach \Angle in {5}
{\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70},
line join = round, line cap = round,c/.style={circle,fill,inner sep=1pt},
same bounding box=A,
declare function={h1=5;h2=0;myR=3;}]
\path[overlay]
(0,0,0) coordinate (O)
(-myR,0,h1) coordinate (H1)
(myR,0,h2) coordinate (H2)
(0,myR,0.5*h1+0.5*h2) coordinate (H3);
\pgfmathsetmacro{\myscreenex}{TDunit("(0,0,1)x(nscreenx,nscreeny,nscreenz)")}
\path[3d coordinate={(L)=-myR*(\myscreenex)},
3d coordinate={(R)=myR*(\myscreenex)}];
\pgfmathsetmacro{\myF}{TDunit("(\myscreenex)x(0,0,1)")}
\pgfmathsetmacro{\myF}{TD("myR*(\myF)")}
\path (\myF) coordinate (F);
\pgfmathsetmacro{\myn}{TDunit("(H2)-(H1)x(0,1,0)")}
\tikzset{3d/plane with normal={(\myn) through (H1) named p},
3d/line with direction={(0,0,1) through (L) named l1},
3d/line with direction={(0,0,1) through (R) named l2},
3d/line with direction={(0,0,1) through (O) named l3},
3d/line with direction={(0,0,1) through (F) named l4}}
\path[3d/intersection of={l1 with p}] coordinate (L');
\path[3d/intersection of={l2 with p}] coordinate (R');
\path[3d/intersection of={l3 with p}] coordinate (O');
\path[3d/intersection of={l4 with p}] coordinate (F');
\path (O) pic{3d/circle on sphere={R=myR,n={(0,0,1)}}};
\draw[3d/visible] (L) -- (L') (R) -- (R');
\pgfmathsetmacro{\myRp}{tddistance("(H2)","(O')")}
\tikzset{3d/define orthonormal dreibein={A={(O')},B={(H3)},C={(H2)}}}
\pgfmathsetmacro{\myphi}{atan2(TD("(0,1,0)o(\myscreenex)"),TD("(1,0,0)o(\myscreenex)"))}
\pgfmathtruncatemacro{\itest}{screendepth(\myn)>0?1:0}
\begin{scope}[x={(ex)},y={(ey)},z={(ez)},shift={(O')}]
\ifnum\itest=1
\draw[3d/visible] (O') circle[x radius=myR,y radius=\myRp];
\else
\draw[3d/hidden]
(90-\myphi:myR and \myRp) arc[start angle=90-\myphi,end angle=90-\myphi-180,x radius=myR,y radius=\myRp];
\draw[3d/visible]
(90-\myphi:myR and \myRp) arc[start angle=90-\myphi,end angle=90-\myphi+180,x radius=myR,y radius=\myRp];
\fi
\end{scope}
\end{tikzpicture}}
\end{document}