P_1 = (2.62, 4.74)
P_2 = (4.28, 2.4)
P_3 = (3.18, 0.68)
O = (1.62, 1.04)
P_4 = (0.5, 3.38)
c = Conic(P_1, P_2, P_3, O, P_4)
ot = Tangent(O, c)
on = OrthogonalLine(O, ot)
Ω = Point(on)
ω = Circle(Ω, O)
D_1 = (4.22, 0)
D_2 = (4.452, -2.254)
d = Line(D_1, D_2)
op_1 = Line(P_1, O)
op_2 = Line(P_2, O)
op_3 = Line(P_3, O)
p_{12} = Line(P_1, P_2)
p_{23} = Line(P_2, P_3)
U = Intersect(d, p_{12})
V = Intersect(d, p_{23})
h = OrthogonalLine(Ω, op_2)
i = OrthogonalLine(Ω, op_3)
j = OrthogonalLine(Ω, op_1)
k = OrthogonalLine(Ω, p_{23})
P'_3 = Mirror(O, i)
P'_2 = Mirror(O, h)
P'_1 = Mirror(O, j)
ou = Line(U, O)
ov = Line(V, O)
p'_{23} = Line(P'_3, P'_2)
V' = Intersect(ov, p'_{23})
p'_{12} = Line(P'_2, P'_1)
U' = Intersect(ou, p'_{12})
a = Line(V', U')
X', Y' = Intersect(ω, a)
ox = Line(X', O)
oy = Line(O, Y')
Y = Intersect(oy, d)
X = Intersect(ox, d)