Propriété des triangles semblables par Thalès

B = (-1.1887024390243914, 0.3487414634146374)
C = (3.3275902439024394, -0.7351609756097538)
A = (0.5053232291670723, 1.8863226248998048)
f = Segment(B, A)
g = Segment(A, C)
h = Segment(C, B)
B' = (5.7372075086578365, 2.6337346648270556)
C' = (3.8366454642713954, 0.4342078044697142)
i = Segment(B', C')
α = Angle(C, B, A)
β = Angle(A, C, B)
γ = Angle(B, A, C)
B'' = Rotate(C', Angle[C, B, A], B')
δ = Angle(C', B', B'')
j = Line(B', B'')
A'' = Rotate(B', (-Angle[A, C, B]), C')
ε = Angle(A'', C', B')
k = Line(C', A'')
A' = Intersect(j, k)
l = Segment(B', A')
m = Segment(A', C')
ζ = Angle(B', A', C')
etape = 0 (slider from 0 to 10, step 1)
n = Segment(C', B')
p = Segment(C', A')
c = Circle(C, Distance[C', A'])
E = Intersect(c, g, 1)
q = Segment(E, C)
d = Circle(C, Distance[B', C'])
D = Intersect(d, h, 1)
r = Segment(C, D)
s = Segment(E, D)
t = Segment(B', C')
a = Line(D, E)
η = Angle(D, E, C)
θ = Angle(C, D, E)
F = Point(a)
ι = Angle(F, E, A)
b = Line(D, F)
e = Line(B, A)
f_1 = Segment(D, E)
g_1 = Segment(B', A')
t1, d_1, b_1, e_1 = Polygon(B, E, D)
t2, e_2, a_1, d_2 = Polygon(A, D, E)
c_1 = Circle(B, Distance[B', A'])
G = Intersect(c_1, f, 1)
h_1 = Circle(B, Distance[B', C'])
H = Intersect(h_1, h, 1)
i_1 = Segment(B, G)
j_1 = Segment(B, H)
k_1 = Segment(G, H)