gain

Comme IC= 2 IB, le chevron dans BCF 
donne vert+bleu= 2×vert donc vert= bleu.
Par les proportions on en déduit que E est
milieu de [CF], donc que bleu=gris.
Les 7 triangles ont donc tous même aire
qui est 1/7 du total.

preuve

preuve1

preuve2

preuve3

vert=bleu

E est milieu de [CF]

vert= gris

I = (3.76, -2.5)
B = (0.76, -2.44)
c = Circle(I, B)
a = Line(B, I)
D = Intersect(c, a, 2)
d = Circle(D, I)
C = Intersect(d, a, 2)
p = Circle(C, B)
k = Circle(B, C)
H = Intersect(k, p, 1)
a' = Mirror(a, B)
A: H
poly1, c_1, a_1, b = Polygon(A, B, C)
e = Line(D, c_1)
f = Line(D, b)
J = Intersect(e, b)
K = Intersect(f, c_1)
g = Segment(I, A)
h = Segment(K, C)
i = Segment(J, B)
E = Intersect(h, i)
F = Intersect(g, h)
G = Intersect(g, i)
poly2, g_1, e_1, f_1 = Polygon(E, F, G)
poly3, f_2, b_1, g_2 = Polygon(B, G, F)
poly4, c_2, g_3, e_2 = Polygon(G, E, C)
poly5, e_3, a_2, f_3 = Polygon(A, F, E)
j = false
l = false
q1, b_2, f_4, c_3, g_4 = Polygon(B, F, C, G)
m = false
t1, c_4, f_5, g_5 = Polygon(F, G, C)
n = false
t2, c_5, a_3, f_6 = Polygon(A, F, C)
o = false