A = (-2.7526149268183873, 3.8459993788032354)
B = (-4, 0)
C = (1, 0)
AB = Segment(A, B)
BC = Segment(B, C)
AC = Segment(C, A)
K = Intersect(LineBisector[A, B], OrthogonalLine[A, AC])
c_K = Circle(K, A)
J = Intersect(LineBisector[A, C], OrthogonalLine[C, BC])
c_J = Circle(J, C)
I = Intersect(LineBisector[B, C], OrthogonalLine[B, AB])
c_I = Circle(I, B)
JK = Segment(K, J)
Ω' = Mirror(A, JK)
F = Mirror(Ω', J)
D = Mirror(Ω', K)
E = Mirror(Ω', I)
DF = Segment(D, F)
EF = Segment(F, E)
DE = Segment(E, D)
D' = Point(c_K)
df' = Line(D', A)
F' = Mirror(A, OrthogonalLine[J, df'])
ef' = Line(F', C)
de' = Line(D', B)
E' = Intersect(de', ef')
α = Angle(A, B, D')
β = Angle(C, A, F')
γ = Angle(B, C, E')