Mostrar la construcción

P_1 = (-0.9223573255406858, 3.2152945831941615)
P_2 = (2.0274620130268546, 1.270397891429932)
A = (0.7388533396528726, 7.045993797975739)
B = (6.222621564482034, 0.6036363636363644)
t_P = Line(A, B)
P = Point(t_P)
C = (-4.634786312548252, -0.9815658457206157)
D = (7.309662381409773, 1.0747608407490836)
t = Line(C, D)
a = Line(P_1, P_2)
X = Intersect(t_P, a)
Y = Intersect(t, a)
D_1, D_2 = PuntosDoblesInvolucion(a, P_1, P_2, X, Y)
c = Line(P, D_1)
T_1 = Intersect(t, c)
d, I = ConicaCuatroPuntosTangente(t_P, P, P_2, P_1, T_1)
b = Line(P, D_2)
T_2 = Intersect(b, t)
e, J = ConicaCuatroPuntosTangente(t_P, P, T_2, P_2, P_1)
f = true

Tool: Puntos Dobles Involucion (command PuntosDoblesInvolucion)
Dar pares de puntos conjugados sobre una recta
Input: l, A, A', B, B'
Output: G, H

$\ell$

A = Point(l)
A' = Point(l)
B = Point(l)
B' = Point(l)
C = Midpoint(A, A')
c = Circle(C, A)
a = OrthogonalLine(C, l)
D = Intersect(c, a, 2)
e = Line(D, B)
f = Line(D, B')
g = OrthogonalLine(C, e)
h = OrthogonalLine(C, f)
D' = Mirror(D, h)
D'_1 = Mirror(D, g)
i = Line(A, D')
j = Line(A', D'_1)
X = Intersect(i, j)
k = Line(A, D'_1)
m = Line(A', D')
Y = Intersect(m, k)
n = Line(X, Y)
E, F = Intersect(c, n)
p = Line(D, F)
q = Line(E, D)
G = Intersect(l, q)
H = Intersect(l, p)

Tool: Conica Cuatro Puntos Tangente (command ConicaCuatroPuntosTangente)
Dar una tangente, el punto de tangencia y tres puntos más
Input: t_P, P, P_1, P_3, P_2
Output: h, X

δ

Recta de Pascal

P = Point(t_P)
a = Line(P_2, P_3)
L = Intersect(a, t_P)
b = Line(L, P_1)
c = Line(P, P_2)
d = Line(P_3, P_1)
M = Intersect(c, d)
e = Line(M, L)
f = Line(P, P_3)
N = Intersect(e, f)
g = Line(P_2, N)
X = Intersect(b, g)
h = Conic(X, P_2, P, P_3, P_1)

Tool: Conica TangentePunto TangentePunto Punto (command ConicaTangentePuntoTangentePuntoPunto)
Tangente punto de tangencia, tangente punto de tangencia, Punto
Input: t_1, P_1, t_2, P_2, P
Output: f

P_1 = Point(t_2)
P_2 = Point(t_1)
a = AngularBisector(P_1, P, P_2)
b = Line(P, P_1)
E = Intersect(b, t_1)
c = Line(P_1, P_2)
F = Intersect(a, c)
d = Line(E, F)
G = Intersect(t_2, d)
e = Line(G, P_2)
H = Intersect(e, a)
f, I = ConicaCuatroPuntosTangente(t_2, P_1, H, P_2, P)