Solution

A = (-2.4393442622950814, -1.2990176293594842)
f = Line(A, xAxis)
B = Point(f)
C = Rotate(B, 60°, A)
g = Segment(A, B)
h = Segment(B, C)
i = Segment(C, A)
F = Point(g)
j = Segment(C, F)
O: (A + B + C) / 3
F' = Rotate(F, 120°, O)
F'' = Rotate(F', 120°, O)
k_{1} = Segment(A, F')
l = Segment(B, F'')
M = Intersect(j, l)
N = Intersect(j, k_{1})
P = Intersect(k_{1}, l)
m = Segment(A, P)
n = Segment(M, B)
p = Segment(C, N)
q = Segment(N, F)
B' = Mirror(B, i)
r = OrthogonalLine(O, m)
D = Intersect(r, m)
c = Circle(O, D)
s = AngularBisector(A, C, F)
d = Circle(B', C)
t = Line(B', N)
I = Intersect(s, t)
a = Line(A, I)
b = OrthogonalLine(I, i)
E = Intersect(b, i)
e = Circle(I, E)
f_1 = Line(O, m)
J = Intersect(f_1, t)
C' = Rotate(O, 60°, B')
c_1 = Circle(B', O, C')
G = Center(c_1)
g_1 = Segment(B', C)
e' = Rotate(e, 120°, O)
e'' = Rotate(e', 120°, O)
H, K = Intersect(c_1, d)
h_1 = Line(C, H)
A' = Mirror(A, h_1)
i_1 = Line(C, A')
F_0 = Intersect(i_1, g)
k = AffineRatio(A, B, F)
rr: Radius[c] / Radius[e]
texte1: "\dfrac{AF}{AB}=" + (LaTeX[k]) + "\qquad\dfrac{r}{r'}=" + (LaTeX[rr]) + ""