我想画一个 Lemoine 椭圆，但是无法确定焦点坐标。代码如下。
\documentclass[10pt]{article}
\usepackage[a4paper,margin=2cm]{geometry}
\usepackage[dvipsnames,x11names]{xcolor}
\renewcommand{\rmdefault}{put}
\usepackage{tikz}
\usetikzlibrary{shapes,fit,positioning,calc,intersections}
\newcommand{\bagisudut}[6][]{%
\path[#1] let
\p1 = ($(#3)!1cm!(#2)$),
\p2 = ($(#3)!1cm!(#4)$),
\p3 = ($(\p1) + (\p2) - (#3)$)
in
($(#3)!#6!(\p3)$) -- ($(\p3)!#5!(#3)$) ;
}
\begin{document}
\begin{tikzpicture}
%\draw[help lines] (-1,-1) grid (10,7);
\coordinate (A) at (0,0);
\coordinate (B) at (7.5,0);
\coordinate (C) at (.5,5);
\draw[thick,Tomato2] (A) node[left,xshift=.1cm,black,yshift=.2cm,black]{A} --(B) node[right,xshift=-.1cm,yshift=.2cm,black]{B} --(C) node[above,xshift=.15cm,yshift=-.1cm,black]{C} --cycle;
\coordinate (P) at ($(B)!.5!(C)$);%median BC
\coordinate (Q) at ($(A)!.5!(B)$);%median AB
\coordinate (D) at ($(A)!.5!(C)$);%median AC
\draw[name path=AP,help lines,ProcessBlue] (A)--(P) ;
\draw[name path=CQ,help lines,ProcessBlue] (C)--(Q);
\draw[name path=BD,ProcessBlue] (B)--(D);
%------------------------------------------------------------------------
\path[name intersections={of = AP and CQ, by=F}];
%------------------------------------------------------------------------
\bagisudut[draw,Peach,name path=sdtC]{A}{C}{B}{1.5}{3.5}
\path[name path=AB] (A)--(B);
\path[name intersections={of = AB and sdtC, by=T1}];
\path[name path=lingk1] (T1) let \p1 = ($(Q)-(T1)$),\n1 = {veclen(\x1,\y1)} in ++(\n1,0) arc (0:360:\n1);
\path[name intersections={of = AB and lingk1, by={T2,T3}}];
\draw[name path=CT3,help lines] (C)--(T3);
\bagisudut[draw,Peach,name path=sdtA]{C}{A}{B}{1.5}{3.5}
\path[name path=BC] (B)--(C);
\path[name intersections={of = BC and sdtA, by=T4}];
\path[name path=lingk2] (T4) let \p1 = ($(P)-(T4)$),\n1 = {veclen(\x1,\y1)} in ++(\n1,0) arc (0:360:\n1);
\path[name intersections={of = BC and lingk2, by={T5,T6}}];
\draw[name path=AT5,help lines] (A)--(T5);
%------------------------------------------------------------------------
\path[name intersections={of = CT3 and AT5, by=E}];
%------------------------------------------------------------------------
\path[name intersections={of = sdtC and sdtA, by=R}];
\path[name intersections={of = CQ and sdtA, by=S}];
\path[name intersections={of = sdtA and CT3, by=T}];
\bagisudut[draw,Peach,name path=sdtB]{C}{B}{A}{1.25}{4.25}
\path[name path=BE] (B)--($(B)!8.5cm!(E)$) ;%(B)--($(B)!9cm!(T)$);
\path[name path=AC] (A)--(C);
\path[name intersections={of = AC and BE, by=G}];
\draw[help lines,name path=BG] (B)--(G);
\path[name intersections={of = sdtA and BG, by=H}];
\path[name intersections={of = sdtA and BD, by=I}];
\coordinate (J) at ($(A)!(R)!(B)$);
\coordinate (K) at ($(B)!(R)!(C)$);
\coordinate (L) at ($(A)!(R)!(C)$);
\draw[thick,Blue4]
let
\p1=( $ (J)-(R) $ )
in
(R) circle ({veclen(\x1,\y1)});
\draw[dashed,help lines,Red1,name path=AK] (A)--(K) ;
\draw[dashed,help lines,Red1,name path=BL] (B)--(L) ;
\draw[dashed,help lines,Red1,name path=CJ] (C)--(J);
\path[name intersections={of = AK and BL, by=M}];
%\path[thick,BlueViolet] (M)--(F)
% node[midway, sloped, draw, ellipse,fit=(M.north east)(F.south west),inner sep=1cm]{};
\draw[PeachPuff4,fill=Cornsilk1] (R) node[below]{O}circle (1.5pt) (E) circle (1.5pt) (F) circle (1.5pt) (J) circle (1.5pt) (K) circle (1.5pt) (L) circle (1.5pt) (M) circle (1.5pt);
\node[right] at (3.5,3.8){\footnotesize\em bisector};%AP
\node[below left] at (-0.15,2.65){\footnotesize\em bisector};%BD
\node[right] at (2.5,-.7){\footnotesize\em bisector};%CQ
\node[above right] at (P){\footnotesize\em median};%AP
\node[above left] at (D){\footnotesize\em median};%BD
\node[below] at (Q){\footnotesize\em median};%CQ
\end{tikzpicture}
\end{document}