A

B

C

Euler line

DC(P)

DC(P)*

L = (-0.7621818181818181, -2.4854545454545427)
M = (8.717818181818185, -2.5054545454545427)
N = (5.9378181818181845, 2.554545454545453)
polígono1, c, a, b = Polygon(L, M, N)
d = TriangleCurve(L, M, N, A^(2) * B^(2) * (-a^(4) * c^(4) + b^(4) * c^(4) + a^(2) * c^(6) - b^(2) * c^(6)) + A * B^(2) * (a^(6) * c^(2) - a^(4) * b^(2) * c^(2) + a^(2) * b^(2) * c^(4) - a^(2) * c^(6)) * C + A^(2) * B * (a^(2) * b^(4) * c^(2) - b^(6) * c^(2) - a^(2) * b^(2) * c^(4) + b^(2) * c^(6)) * C + A * B * (-a^(6) * b^(2) + a^(2) * b^(6) + a^(4) * b^(2) * c^(2) - a^(2) * b^(4) * c^(2)) * C^(2) + B^(2) * (a^(6) * b^(2) - a^(4) * b^(4) - a^(6) * c^(2) + a^(4) * c^(4)) * C^(2) + A^(2) * (a^(4) * b^(4) - a^(2) * b^(6) + b^(6) * c^(2) - b^(4) * c^(4)) * C^(2) = 0)
X_2 = TriangleCenter(L, M, N, 2)
X_4 = TriangleCenter(L, M, N, 4)
X_{69} = TriangleCenter(L, M, N, 69)
e = Line(X_2, X_4)
f = Conic(L, M, N, X_2, X_{69})
P = Point(e)
DCP = DCPCeviano(L, M, N, P)
DCP' = ConjugadoIsogonal(L, M, N, DCP)
DCP'' = Mirror(DCP', X_2)
Q = Mirror(X_2, DCP'')
X = Trilinear(L, M, N, -b * (a^(2) + b^(2)) * c * (a^(2) + c^(2)) * (a^(4) - b^(4) + c^(4)) * (a^(6) - a^(4) * (b^(2) + c^(2)) - (b^(2) - c^(2)) * (b^(2) + c^(2))^(2) + a^(2) * (b^(4) - c^(4))), a * (a^(2) + b^(2)) * c * (b^(2) + c^(2)) * (-a^(4) + b^(4) + c^(4)) * (a^(6) + a^(4) * (-b^(2) + c^(2)) - (b^(2) - c^(2))^(2) * (b^(2) + c^(2)) + a^(2) * (b^(4) - c^(4))), a * b * (a^(2) + b^(2) - c^(2)) * (a^(2) + c^(2)) * (b^(2) + c^(2)) * (a^(4) - b^(4) + c^(4)) * (-a^(4) + b^(4) + c^(4)))
lugar1 = Locus(DCP', P)

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: 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)

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: 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)