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\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
numeric u; u = 144;
path base; base = fullcircle rotated 180 scaled u;
path cardioid;
cardioid = for t = 0 step 1/4 until length base:
point 0 of base reflectedabout(precontrol t of base, postcontrol t of base) ..
endfor cycle;
numeric t; t = 5.4;
pair A, M, P, P', Q, Q', R;
A = point 0 of base;
Q = point t of base;
Q' = point t-4 of base;
P = A reflectedabout(precontrol t of base, postcontrol t of base);
P' = A reflectedabout(precontrol t-4 of base, postcontrol t-4 of base);
M = 1/2[P, P'];
R = whatever[P, Q] = whatever[P', Q'];
%draw Q' -- R -- Q withcolor 3/4;
draw 3[postcontrol t of base, precontrol t of base]
-- 5[precontrol t of base, postcontrol t of base] withcolor 3/4;
%draw 5[postcontrol t-4 of base, precontrol t-4 of base]
% -- 3[precontrol t-4 of base, postcontrol t-4 of base] withcolor 3/4;
draw fullcircle scaled 2 abs (Q-A) shifted Q withcolor 7/8;
%
%draw P' -- Q' -- Q -- P -- cycle;
draw A -- Q -- P -- cycle;
draw base withcolor 2/3 blue;
draw origin withpen pencircle scaled dotlabeldiam withcolor 2/3 blue;
draw cardioid withcolor 1/4[white, 1/2 red];
dotlabel.ulft("$A$", A);
%dotlabel.ulft("$M$", M);
dotlabel.top ("$P$", P);
%dotlabel.llft("$P'$", P');
dotlabel.urt ("$Q$", Q);
%dotlabel.bot ("$Q'$", Q');
%dotlabel.lrt ("$R$", R);
endfig;
\end{mplibcode}
\end{document}
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