\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
vardef through(expr a, b, o) =
save t; numeric t; t = 1+o/abs(a-b);
t[b,a] -- t[a,b]
enddef;
vardef circumcircle(expr T) =
save m; pair m;
m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T
= whatever * (point 1 of T - point 2 of T) rotated 90 shifted point 3/2 of T;
fullcircle scaled 2 abs (point 0 of T - m) shifted m
enddef;
beginfig(1);
path T; T = origin -- 377 dir 10 -- 233 dir 70 -- cycle;
pair m;
m = whatever * (point 0 of T - point 1 of T) rotated 90 shifted point 1/2 of T
= whatever * (point 2 of T - point 3 of T) rotated 90 shifted point 5/2 of T;
drawoptions(withcolor 3/4);
draw unitsquare scaled 5 rotated angle (point 1 of T-point 0 of T) shifted point 1/2 of T;
draw unitsquare scaled 5 rotated angle (point 2 of T-point 1 of T) shifted point 3/2 of T;
draw unitsquare scaled 5 rotated angle (point 0 of T-point 2 of T) shifted point 5/2 of T;
drawoptions(dashed evenly scaled 1/4 withcolor 1/2);
draw through(point 1/2 of T, m, 10);
draw through(point 3/2 of T, m, 10);
draw through(point 5/2 of T, m, 10);
drawoptions();
draw circumcircle(T) withcolor 2/3 red;
draw T;
draw m withpen pencircle scaled dotlabeldiam; label("$m$", m + 10 dir 12);
vardef mark_equal(expr a, b, n) =
save m, s; picture m; m = image(
numeric s; 2s = n - 1; for t=-s upto s:
draw (down--up) scaled 2 rotated -13 shifted (t,0)
withpen pencircle scaled 1/4;
endfor
);
draw m rotated angle (b-a) shifted 1/4[a,b];
draw m rotated angle (b-a) shifted 3/4[a,b];
enddef;
mark_equal(point 0 of T, point 1 of T, 1);
mark_equal(point 1 of T, point 2 of T, 2);
mark_equal(point 2 of T, point 0 of T, 3);
