M=m

N= n

A = (-1.9234792033599797, 1.619658866984125)
f = Line(A, xAxis)
B = Point(f)
c = Circle(A, B)
C = Point(f)
g = Line(C, xAxis)
D = Point(g)
d = Circle(C, D)
h = OrthogonalLine(A, g)
i = OrthogonalLine(C, g)
F = Intersect(c, h, 2)
G = Intersect(d, i, 1)
j = Line(F, G)
k = OrthogonalLine(C, j)
G' = Mirror(G, k)
l = Tangent(F, c)
m = Tangent(G', d)
H_{1} = Intersect(l, m)
n = OrthogonalLine(H_{1}, g)
H = Intersect(g, n)
PA: A
PB: B
PC: C
PD: D
D' = Mirror(D, C)
U = (4.362006602317744, 0.8865121256806453)
PU: U
α = Angle(D', H, U)
U'_{1} = Rotate(U, (-α), H)
a = AffineRatio(H, U'_{1}, D')
D'_{1} = Dilate(D, a, H)
E = Rotate(D'_{1}, α, H)
p = LineBisector(E, U)
I = Intersect(p, g)
e = Circle(I, U)
M' = Point(d)
q = Line(M', U)
M, N = Intersect(c, q)
r = OrthogonalLine(C, q)
N' = Mirror(M', r)
S = Point(c)
PM': M'
PS: S
s = Line(S, M')
t = Line(S, N')
b = Line(S, U)
f_1 = Line(S, N)
g_1 = Line(S, M)
h_1 = OrthogonalLine(A, t)
i_1 = OrthogonalLine(A, b)
j_1 = OrthogonalLine(A, s)
m' = Mirror(S, j_1)
n' = Mirror(S, h_1)
u = Mirror(S, i_1)
k_1 = Line(n', m')
Q = Intersect(q, k_1)
l_1 = Line(u, Q)
m_1 = OrthogonalLine(A, l_1)
u' = Mirror(u, m_1)
n_1 = Line(u', S)
U' = Intersect(n_1, q)
PU': U'