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$\Gamma$

$\Phi$

m = true
P_1 = (-2.102000402051686, 40.3420383527754)
P_2 = (-9.91641492237005, 12.210146079629231)
P_3 = (0.6250119418205278, 2.8179630338279305)
A = (46.34736962392213, 23.15032640807496)
B = (36.6635216486675, 19.987138485154674)
c = Circle(A, B)
C = (-32.60407157990623, -10.351051024069623)
D = (27.543343021592392, -10.351051024069623)
δ = Line(C, D)
F, J = Intersect(c, δ)
a = Line(P_1, P_2)
b = Line(P_1, P_3)
d = Line(P_2, P_3)
K = Intersect(δ, a)
L = Intersect(b, δ)
M = Intersect(d, δ)
E = Midpoint(K, L)
e = Circle(E, K)
T = involucionBis(δ, e, c, M)
t_1 = Line(P_1, T)
G = Midpoint(P_2, P_3)
f = Circle(G, P_3)
g = Polar(M, f)
U = Intersect(g, d)
h = Polar(M, c)
V = Intersect(h, δ)
i = Line(U, V)
j = Line(M, P_1)
W = Intersect(j, i)
H = Midpoint(W, M)
k = Circle(H, M)
l = Polar(P_1, k)
P = Intersect(l, j)
p, I = ConicaCuatroPuntosTangente(t_1, P_1, P_2, P_3, P)

Tool: involucionBis
Dar una recta, dos circunferencias y un punto en la recta
Input: a, c, d, M
Output: M'

M = Point(a)
b = Polar(M, c)
P = Intersect(a, b)
e = Polar(M, d)
G = Intersect(e, a)
f = Polar(P, d)
P' = Intersect(f, a)
g = Polar(G, c)
Q' = Intersect(g, a)
H = Midpoint(P', Q')
h = Circle(H, Q')
i = Polar(M, h)
M' = Intersect(i, a)

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)