sol 1 I

sol 2 J_a

sol 3 J_b

sol 4 J_c

4 sols

A = (0.1, 1.42)
B = (-1.6401903377804063, 0.6167636604163756)
C = (2.14, -0.46)
F = (-1.66, -0.44)
c_a = Circle(A, F)
c_b = Circle(B, F)
c_c = Circle(C, F)
D = (0.6334576696146447, -0.906022160032811)
f = Circle(F, D)
B_1 = Mirror(F, B)
A_1 = Mirror(F, A)
C_1 = Mirror(F, C)
FB = Segment(B_1, F)
FA = Segment(F, A_1)
FC = Segment(F, C_1)
B'_1 = Mirror(B_1, f)
A'_1 = Mirror(A_1, f)
C'_1 = Mirror(C_1, f)
d_c = OrthogonalLine(C'_1, FC)
d_a = OrthogonalLine(A'_1, FA)
d_b = OrthogonalLine(B'_1, FB)
A' = Intersect(d_c, d_b)
C' = Intersect(d_a, d_b)
B' = Intersect(d_c, d_a)
ai = AngularBisector(C', A', B')
ci = AngularBisector(B', C', A')
I = Intersect(ci, ai)
cj = OrthogonalLine(C', ci)
aj = OrthogonalLine(A', ai)
J_b = Intersect(cj, aj)
J_a = Intersect(ai, cj)
Jc = Intersect(ci, aj)
ib = OrthogonalLine(I, d_b)
ic = OrthogonalLine(I, d_c)
ia = OrthogonalLine(I, d_a)
X'_a = Intersect(d_a, ia)
X'_b = Intersect(d_b, ib)
X'_c = Intersect(d_c, ic)
X_c = Mirror(X'_c, f)
X_b = Mirror(X'_b, f)
X_a = Mirror(X'_a, f)
d_I = Circle(X_a, X_c, X_b)
F'_I = Center(d_I)
c_i = Circle(I, X'_c)
m_i = Point(d_I)
fm_i = Line(F'_I, m_i)
t_i = LineBisector(m_i, F)
M_i = Intersect(t_i, fm_i)
Γ_i = Locus(M_i, m_i)
jab = OrthogonalLine(J_a, d_b)
jaa = OrthogonalLine(J_a, d_a)
jac = OrthogonalLine(J_a, d_c)
Y'a_b = Intersect(jab, d_b)
Y'a_c = Intersect(jac, d_c)
Y'a_a = Intersect(jaa, d_a)
c_{ja} = Circle(J_a, Y'a_c)
Ya_b = Mirror(Y'a_b, f)
Ya_c = Mirror(Y'a_c, f)
Ya_a = Mirror(Y'a_a, f)
d_{ja} = Circle(Ya_a, Ya_b, Ya_c)
F'_{ja} = Center(d_{ja})
m_{ja} = Point(d_{ja})
f'm_{ja} = Line(F'_{ja}, m_{ja})
t_{ja} = LineBisector(F, m_{ja})
M_{ja} = Intersect(t_{ja}, f'm_{ja})
Γ_{ja} = Locus(M_{ja}, m_{ja})
i = true
a = false
jbb = OrthogonalLine(J_b, d_b)
jbc = OrthogonalLine(J_b, d_c)
jba = OrthogonalLine(J_b, d_a)
Y'b_a = Intersect(jba, d_a)
Y'b_b = Intersect(jbb, d_b)
Y'b_c = Intersect(jbc, d_c)
c_{jb} = Circle(J_b, Y'b_b)
Yb_c = Mirror(Y'b_c, f)
Yb_b = Mirror(Y'b_b, f)
Yb_a = Mirror(Y'b_a, f)
d_{jb} = Circle(Yb_b, Yb_a, Yb_c)
F'_{jb} = Center(d_{jb})
m_{jb} = Point(d_{jb})
f'm_{jb} = Line(F'_{jb}, m_{jb})
t_{jb} = LineBisector(m_{jb}, F)
M_{jb} = Intersect(t_{jb}, f'm_{jb})
Γ_{jb} = Locus(M_{jb}, m_{jb})
b = false
jca = OrthogonalLine(Jc, d_a)
jcc = OrthogonalLine(Jc, d_c)
jcb = OrthogonalLine(Jc, d_b)
Y'c_a = Intersect(d_a, jca)
Y'c_c = Intersect(d_c, jcc)
Y'c_b = Intersect(d_b, jcb)
c_{jc} = Circle(Jc, Y'c_c)
Yc_a = Mirror(Y'c_a, f)
Yc_b = Mirror(Y'c_b, f)
Yc_c = Mirror(Y'c_c, f)
d_{jc} = Circle(Yc_c, Yc_b, Yc_a)
F'_{jc} = Center(d_{jc})
m_{jc} = Point(d_{jc})
f'm_{jc} = Line(F'_{jc}, m_{jc})
t_{jc} = LineBisector(m_{jc}, F)
M_{jc} = Intersect(f'm_{jc}, t_{jc})
Γ_{jc} = Locus(M_{jc}, m_{jc})
c = false
A'B'C', c', a', b' = Polygon(A', B', C')
t = false