A = (-2.714754098360655, 1.5140971247388757)
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)
P = Point(g)
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
PP: P
e = Circle(H_{1}, F)
D' = Mirror(D, C)
a = AffineRatio(H, P, D)
P' = Dilate(D', a, H)
Ω = Midpoint(P', P)
p = Circle(Ω, P)
X = (-4.485245901639342, 3.2845889280175635)
X' = (6.059016393442622, 0.9829495837552676)
q = Line(X, X')
N_1, M_1 = Intersect(c, q)
N_2, M_2 = Intersect(d, q)
N, M = Intersect(p, q)
PN_1: N_1
PM_1: M_1
PN: N
PM: M
PN_2: N_2
PM_2: M_2