prop

sol 1

sol 2

F = (12, 8)
D = (9, 5)
m = LineBisector(F, D)
f = Line(D, xAxis)
E = Point(f)
k = Segment(E, F)
q = LineBisector(k)
A = (1, 9)
C = Intersect(xAxis, yAxis)
B = Point(xAxis)
β = Angle(A, B, C)
p = Ray(E, Rotate[F, β - π / 2, E])
J = Intersect(q, p)
α = Angle(C, A, B)
n = Ray(F, Rotate[D, α - π / 2, F])
I = Intersect(m, n)
L = Midpoint(I, J)
d_1 = Circle(L, I)
c = Segment(A, B)
g = Circle(J, c / 2)
M_2, M_1 = Intersect(g, d_1)
h_2 = Segment(M_2, J)
i_2 = Line(F, h_2)
k_2 = OrthogonalLine(J, i_2)
B'_2 = Mirror(F, k_2)
m_2 = Line(B'_2, E)
j_2 = OrthogonalLine(I, i_2)
A'_2 = Mirror(F, j_2)
n_2 = Line(A'_2, D)
C'_2 = Intersect(n_2, m_2)
b = Segment(A, C)
a = Segment(C, B)
j = Segment(D, E)
l = Segment(F, D)
γ = Angle(B, C, A)
c_{2} = Circle(I, F)
d = Circle(J, F)
A' = Point(c_{2})
r = Line(A', F)
s = OrthogonalLine(J, r)
B' = Mirror(F, s)
t = Line(A', D)
a_{1} = Line(B', E)
C' = Intersect(t, a_{1})
b_{1} = Segment(A', B')
e = Segment(B', C')
f_1 = Segment(C', A')
g_1 = Ray(D, Rotate[E, γ - π / 2, D])
h_1 = LineBisector(D, E)
G = Intersect(h_1, g_1)
c_1 = Circle(G, D)
H = Midpoint(A', F)
K = Midpoint(F, B')
i_1 = Segment(I, H)
j_1 = Segment(J, K)
k_1 = Segment(J, I)
u = Vector(K, J)
M = Translate(H, u)
l_1 = Segment(M, J)
h = Segment(M_1, J)
i = Line(F, h)
m_1 = OrthogonalLine(I, i)
n_1 = OrthogonalLine(J, i)
A'_1 = Mirror(F, m_1)
B'_1 = Mirror(F, n_1)
p_1 = Segment(A'_1, B'_1)
q_1 = Line(A'_1, D)
r_1 = Line(B'_1, E)
C'_1 = Intersect(q_1, r_1)
t_1 = Segment(B'_1, C'_1)
e_1 = Segment(C'_1, A'_1)
rc_1 = AffineRatio(B'_1, A'_1, F)
F_1 = Dilate(A, rc_1, B)
rb_1 = AffineRatio(A'_1, C'_1, D)
D_1 = Dilate(C, rb_1, A)
s_1 = Segment(D_1, F_1)
ra_1 = AffineRatio(C'_1, B'_1, E)
E_1 = Dilate(B, ra_1, C)
f_2 = Segment(F_1, E_1)
g_2 = Segment(E_1, D_1)
o = false
v = false
w = false
l_2 = Segment(A'_2, B'_2)
p_2 = Segment(B'_2, C'_2)
q_2 = Segment(A'_2, C'_2)
r_2 = Segment(M, H)
rc_2 = AffineRatio(B'_2, A'_2, F)
F_2 = Dilate(A, rc_2, B)
rb_2 = AffineRatio(A'_2, C'_2, D)
D_2 = Dilate(C, rb_2, A)
ra_2 = AffineRatio(C'_2, B'_2, E)
E_2 = Dilate(B, ra_2, C)
s_2 = Segment(D_2, F_2)
t_2 = Segment(F_2, E_2)
a_2 = Segment(E_2, D_2)