sol

C = (1, 0)
B = (-4, 0)
BC = Segment(B, C)
P = Point(BC)
A = (-3.359005077482618, 3.816124577200968)
ac = Line(A, C)
M = Midpoint(P, Mirror[P, ac])
ab = Line(A, B)
N = Midpoint(P, Mirror[P, ab])
mn = Line(N, M)
c = Circle(A, B, C)
O = Center(c)
oa = Line(A, O)
AB = Segment(A, B)
AC = Segment(A, C)
AMON, a, n, o, m = Polygon(A, N, O, M)
ABC, c_1, a_1, b = Polygon(A, B, C)
PN = Segment(N, P)
PM = Segment(P, M)
OM = Segment(M, O)
ON = Segment(O, N)
r: AMON / ABC
texte1: "\frac{aire(AMON)}{aire(ABC)}=" + (LaTeX[r]) + ""
d = Circle(A, N, P)
MN = Segment(N, M)
AP = Segment(A, P)
H = Midpoint(A, Mirror[A, BC])
H' = Midpoint(A, Mirror[A, MN])
AH' = Segment(A, H')
I = Intersect(oa, mn)
α = Angle(A, I, N)
β = Angle(A, P, B)
bc = Line(B, C)
AH = Segment(A, H)
NI = Segment(I, N)
BH = Segment(H, B)
AI = Segment(A, I)
OI = Segment(O, I)
e = true