Apollonius circle

[PDF] [TEX]

\documentclass{standalone}
\usepackage{tkz-euclide}
\usepackage{tkz-elements}
\begin{document} 
    
\begin{elements}
   scale = 0.5
   z.A            = point: new (0,0)
   z.B            = point: new (6,0)
   z.C            = point: new (0.8,4) ; id ()
     T            = triangle: new(A,B,C)
   z.O            = T: circum_center ()
   _,_,z.Mc       = T: medial_tr ()
   z.Ja,z.Xa,_,_,
   z.Jb,z.Xb,_,_,
   z.Jc,z.Xc,_,_  = T: circle_ex_all()
   z.N            = T: euler_center ()
   z.L            = T: lemoine_center ()
   z.S            = T: spieker_center () ; id ()
   z.Ap           = intersection_ll_ (O,L,N,S); id ()
   z.x            = ll_from_ (Ap,N,Mc) ; id ()
   z.rAp          = intersection_ll_ (Ap,x,Mc,S)
\end{elements}

 \begin{tikzpicture}
     \tkzGetNodes
     \tkzDrawLines[red](Ap,L N,Ap Ap,rAp Mc,rAp Mc,N)
     \tkzDrawLines[teal,add=1 and 1](A,B A,C B,C)
     \tkzDrawCircles(Ja,Xa Jb,Xb Jc,Xc)
     \tkzDrawCircle[purple](Ap,rAp)
     \tkzDrawPoints(A,B,C,Ja,Jb,Jc)
     \tkzDrawPoints[red](N,O,L,S,Ap,rAp)
 \end{tikzpicture}
\end{document}