F*

C*

B*

A*

$t_{P_1}$

$t_{P_2}$

$t_{P_3}$

F = (5.074064899677979, 0.41380154561487487)
P_1 = (3.3024523160762946, 6.049669764589363)
P_2 = (7.029972752043598, -1.438068655029168)
P_3 = (-6.269011642308644, -3.3642514640457635)
polígono1, p_2, p_3, p_1 = Polygon(P_3, P_1, P_2)
a = Line(P_1, P_2)
b = Line(P_2, P_3)
c = Line(P_3, P_1)
A = ConjugadoIsogonal(P_1, P_2, P_3, F)
d = OrthogonalLine(A, a)
e = OrthogonalLine(A, b)
f = OrthogonalLine(A, c)
B = Intersect(a, d)
C = Intersect(f, c)
D = Intersect(e, b)
g = Segment(C, B)
h = Segment(D, B)
i = Segment(D, C)
j = AngularBisector(D, C, B)
k = AngularBisector(C, B, D)
I = Intersect(k, j)
l = OrthogonalLine(I, g)
m = OrthogonalLine(I, h)
n = OrthogonalLine(I, i)
A_1 = Intersect(g, l)
B_1 = Intersect(m, h)
C_1 = Intersect(i, n)
e_1 = Segment(A_1, B_1)
g_1 = Segment(C_1, B_1)
f_1 = Segment(A_1, C_1)
p = Line(A, A_1)
q = Line(A, B_1)
r = Line(A, C_1)
t_1 = OrthogonalLine(P_1, p)
t_2 = OrthogonalLine(P_2, q)
t_3 = OrthogonalLine(P_3, r)
A' = Intersect(t_3, t_2)
B' = Intersect(t_1, t_3)
C' = Intersect(t_1, t_2)
S_1 = Mirror(F, t_1)
b_1 = Line(S_1, P_1)
S_2 = Mirror(F, t_2)
c_1 = Line(S_2, P_2)
F' = Intersect(b_1, c_1)
O = Midpoint(F, F')
P'_1 = Mirror(P_1, O)
P'_2 = Mirror(P_2, O)
d_1 = Conic(P_1, P_2, P_3, P'_1, P'_2)

Tool: Conjugado Isogonal (command ConjugadoIsogonal)
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: G

P*

polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(P, b)
e = OrthogonalLine(P, a)
f = OrthogonalLine(P, c)
g = Line(A, B)
h = Line(B, C)
i = Line(C, A)
D = Intersect(g, f)
E = Intersect(d, i)
F = Intersect(h, e)
k = Line(E, F)
l = Line(F, D)
n = OrthogonalLine(B, l)
p = OrthogonalLine(C, k)
G = Intersect(n, p)