DC(P)

DEF cevian triangle of P
D'E'F' dual triangle of DEF
DC(P) tripolo of d wrt ABC
D'E'F' circum-anticevian triangle of DC(P)

A = (-0.10145124716553294, -1.1309841269841265)
B = (8.78, -1.38)
C = (5.358548752834468, 4.009015873015874)
polígono1, c, a, b = Polygon(A, B, C)
P = (3.035660770975059, 0.8000136054421746)
d_2 = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
D = Intersect(g, d_2)
E = Intersect(e, h)
F = Intersect(i, f)
polígono2, f_1, d_1, e_1 = Polygon(D, E, F)
D' = TrianguloDual(A, B, C, D, E, F)
E' = TrianguloDual(A, B, C, E, F, D)
F' = TrianguloDual(A, B, C, F, D, E)
polígono3, f', d', e' = Polygon(D', E', F')
k = Circle(A, B, C)
j = Line(A, D')
A' = Intersect(d_2, j)
l = Line(B, E')
B' = Intersect(e, l)
m = Line(C, F')
C' = Intersect(f, m)
d = Line(B', C')
DCP = Tripolo(A, B, C, d)

Tool: Triangulo Dual (command TrianguloDual)
Dar ABC y DEF, determina el vértice D' del triangulo dual D'E'F' de DEF
Input: A, B, C, D, E, F
Output: D'

polígono2, f, d, e = Polygon(D, E, F)
g = Line(A, d)
h = AngularBisector(B, A, C)
g' = Mirror(g, h)
k = Circle(A, B, C)
O = Center(k)
i = OrthogonalLine(O, g')
D' = Mirror(A, i)

Tool: Tripolo
Dados tres puntos y una recta, determina el tripolo de la recta respecto al triángulo de vértices los tres puntos.
Input: A, B, C, m
Output: U

n = Line(A, C)
p = Line(C, B)
K = Intersect(n, m)
N = Intersect(m, p)
A_1 = Midpoint(C, B)
c_1 = Circle(A_1, B)
a_1 = Polar(N, c_1)
R = Intersect(a_1, p)
r = Line(A, R)
S = Midpoint(A, C)
s = Circle(S, A)
t = Polar(K, s)
T = Intersect(n, t)
b_1 = Line(T, B)
U = Intersect(r, b_1)

Tool: Triangulo Ceviano (command TrianguloCeviano)
Dar ABC y P
Input: A, B, C, P
Output: polígono2, A', B', C'

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(A, P)
h = Line(B, P)
i = Line(C, P)
A' = Intersect(d, g)
B' = Intersect(e, h)
C' = Intersect(f, i)
polígono2, f_1, d_1, e_1 = Polygon(A', B', C')

Tool: TrianguloCircunAnticeviano
Dar ABC y P
Input: A, B, C, P
Output: A_1, B_1, C_1, polígono3

polígono2, D, E, F = TrianguloCeviano(A, B, C, P)
d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(F, D)
h = Line(D, E)
i = Line(E, F)
A' = Intersect(d, i)
B' = Intersect(e, g)
C' = Intersect(f, h)
k = Line(A, A')
l = Line(B, B')
m = Line(C, C')
p_1 = Circle(A, B, C)
O = Center(p_1)
n = OrthogonalLine(O, k)
q = OrthogonalLine(O, l)
r = OrthogonalLine(O, m)
A_1 = Mirror(A, n)
B_1 = Mirror(B, q)
C_1 = Mirror(C, r)
polígono3, c'_1, a'_1, b'_1 = Polygon(A_1, B_1, C_1)

Tool: DCPCeviano
Dar ABC y P, determina DC(P)
Input: A, B, C, P
Output: DCP

DC(P)

d_2 = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
D = Intersect(g, d_2)
E = Intersect(e, h)
F = Intersect(i, f)
E' = TrianguloDual(A, B, C, E, F, D)
F' = TrianguloDual(A, B, C, F, D, E)
l = Line(B, E')
B' = Intersect(e, l)
m = Line(C, F')
C' = Intersect(f, m)
d = Line(B', C')
DCP = Tripolo(A, B, C, d)