triangle et point de Napoléon

triangles semblables

Point de Fermat

C = (-0.7593442622950825, 3.377047944411003)
A = Point(xAxis)
B = Point(xAxis)
AB = Segment(A, B)
AC = Segment(C, A)
BC = Segment(C, B)
PC: C
A' = Rotate(B, 60°, C)
B' = Rotate(C, 60°, A)
C' = Rotate(A, 60°, B)
A'B = Segment(A', B)
BC' = Segment(B, C')
AC' = Segment(C', A)
AB' = Segment(A, B')
B'C = Segment(B', C)
A'C = Segment(C, A')
I: (B + C + A') / 3
J: (A + C + B') / 3
K: (A + B + C') / 3
IJ = Segment(I, J)
JK = Segment(J, K)
IK = Segment(K, I)
bb'_{1} = Line(B, B)
cc' = Line(C, C')
T = Intersect(cc', bb'_{1})
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
C_1 = Intersect(Line[J, Rotate[I, α, J]], Line[I, Rotate[J, (-β), I]])
B_1 = Intersect(Line[I, Rotate[K, γ, I]], Line[K, Rotate[I, (-α), K]])
JC_1 = Segment(J, C_1)
IC_1 = Segment(C_1, I)
KB_1 = Segment(K, B_1)
IB_1 = Segment(I, B_1)
A_1 = Intersect(Line[K, Rotate[J, β, K]], Line[J, Rotate[K, (-γ), J]])
JA_1 = Segment(J, A_1)
KA_1 = Segment(A_1, K)
c_C = Circle(J, I, C_1)
c_B = Circle(I, B_1, K)
c_A = Circle(A_1, K, J)
D = Center(c_A)
E = Center(c_B)
F = Center(c_C)
DE = Segment(D, E)
EF = Segment(E, F)
DF = Segment(F, D)
O = Mirror(J, DF)
abc = Circle(O, A)
a = false
c = true
b = false
c_I = Circle(C, A', B)
c_K = Circle(C', A, B)
c_J = Circle(B', C, A)
F_e = Mirror(B, IK)
bb' = Line(B', B)
aa' = Line(A, A')
bj = Line(B, J)
ck = Line(C, K)
ai = Line(A, I)
N_a = Intersect(ai, bj)