Cónica dados un foco y tres tangentes

Mostrar la construcción

F = (11.88277241572817, -1.5036695422280106)
B = (5.313883517203822, 1.539145651781165)
A = (16.079480766826244, -10.70374109002895)
t_1 = Line(A, B)
D = (26.001757630595044, 4.86991955266908)
C = (2.7059771678335123, -0.17749954759593267)
t_2 = Line(C, D)
H = (21.73086454575543, -7.640777362517703)
E = (18.304584010723516, 5.6121440648378575)
t_3 = Line(E, H)
S_1 = Mirror(F, t_1)
S_2 = Mirror(F, t_2)
S_3 = Mirror(F, t_3)
c = Circle(S_1, S_2, S_3)
F' = Center(c)
a = Line(S_1, F')
P_1 = Intersect(a, t_1)
b = Line(S_2, F')
P_2 = Intersect(t_2, b)
d = Line(F', S_3)
P_3 = Intersect(t_3, d)
O = Midpoint(F, F')
I = Mirror(P_2, O)
G = Mirror(P_1, O)
e = Conic(P_1, P_2, P_3, G, I)
f = true