box -2,-2,18,8
A B C triangle 13,5,12
c1 = circle(A, B, C)
D = center(c1)
c2 = incircle(A, B, C)
E = center(c2)
F = intersection(line(A.C), perpendicular(line(A.C), D))
G = point(circle(A, B, C), arg(line(D.F)):)
H = midpoint(F.G)
c3 = circle(H, radius(incircle(A, B, C)))

I = projection(E, line(B.C))
J = projection(E, line(A.B))
K = projection(E, line(A.C))
L = intersection(line(A.B), line(K.E))
M = projection(L, line(B.C))
draw
  (A.B.C)
  c1 0: 180:
  c2
  c3
  D.G dashed
  E.I dashed
  E.J dashed
  K.L dashed
  L.M dashed
  A; B; C; D; E; F; G; H; I; J; K; L
end

label
  A, C, B right
  A -90:; B -90:; C 0:; D -90:; E -45:; F -30:; G 90:; H 0:; I 0:; J -90:; K 90:; L -90:; M 0:
  E, I, B right
  A, J, E right
  E, K, A right
  M, L, E right
  B, A, C double
  J, E, L double
  B, L, M double
end