C

B

A

orthotransversal of P wrt ABC

orthotransversal of P wrt DEF

Euler line

K006=pK(X6, X4)

N = (15.316775962584915, 11.09659250972259)
M = (22.342998410860737, -3.8803838374678756)
L = (-3.5159172723009906, -2.941358119453886)
polígono1, c, a, b = Polygon(L, M, N)
f = TriangleCurve(L, M, N, 2 * a^(4) * A^(3) * B^(2) * c^(4) - 2 * A^(3) * b^(4) * B^(2) * c^(4) + 2 * a^(4) * A^(2) * B^(3) * c^(4) - 2 * A^(2) * b^(4) * B^(3) * c^(4) - 4 * a^(2) * A^(3) * B^(2) * c^(6) + 4 * A^(2) * b^(2) * B^(3) * c^(6) + 2 * A^(3) * B^(2) * c^(8) - 2 * A^(2) * B^(3) * c^(8) + a^(6) * A^(3) * b^(2) * B * C - 3 * a^(4) * A^(3) * b^(4) * B * C + 3 * a^(2) * A^(3) * b^(6) * B * C - A^(3) * b^(8) * B * C + a^(8) * A^(2) * B^(2) * C - 2 * a^(6) * A^(2) * b^(2) * B^(2) * C + 2 * a^(2) * A^(2) * b^(6) * B^(2) * C - A^(2) * b^(8) * B^(2) * C + a^(8) * A * B^(3) * C - 3 * a^(6) * A * b^(2) * B^(3) * C + 3 * a^(4) * A * b^(4) * B^(3) * C - a^(2) * A * b^(6) * B^(3) * C - a^(6) * A^(3) * B * c^(2) * C + 3 * a^(2) * A^(3) * b^(4) * B * c^(2) * C - 2 * A^(3) * b^(6) * B * c^(2) * C - a^(6) * A^(2) * B^(2) * c^(2) * C + 3 * a^(4) * A^(2) * b^(2) * B^(2) * c^(2) * C - 3 * a^(2) * A^(2) * b^(4) * B^(2) * c^(2) * C + A^(2) * b^(6) * B^(2) * c^(2) * C + 2 * a^(6) * A * B^(3) * c^(2) * C - 3 * a^(4) * A * b^(2) * B^(3) * c^(2) * C + A * b^(6) * B^(3) * c^(2) * C + 3 * a^(4) * A^(3) * B * c^(4) * C - 3 * a^(2) * A^(3) * b^(2) * B * c^(4) * C - a^(4) * A^(2) * B^(2) * c^(4) * C + A^(2) * b^(4) * B^(2) * c^(4) * C + 3 * a^(2) * A * b^(2) * B^(3) * c^(4) * C - 3 * A * b^(4) * B^(3) * c^(4) * C - 3 * a^(2) * A^(3) * B * c^(6) * C + 2 * A^(3) * b^(2) * B * c^(6) * C + a^(2) * A^(2) * B^(2) * c^(6) * C - A^(2) * b^(2) * B^(2) * c^(6) * C - 2 * a^(2) * A * B^(3) * c^(6) * C + 3 * A * b^(2) * B^(3) * c^(6) * C + A^(3) * B * c^(8) * C - A * B^(3) * c^(8) * C - 2 * a^(4) * A^(3) * b^(4) * C^(2) + 4 * a^(2) * A^(3) * b^(6) * C^(2) - 2 * A^(3) * b^(8) * C^(2) - a^(8) * A^(2) * B * C^(2) + a^(6) * A^(2) * b^(2) * B * C^(2) + a^(4) * A^(2) * b^(4) * B * C^(2) - a^(2) * A^(2) * b^(6) * B * C^(2) + a^(6) * A * b^(2) * B^(2) * C^(2) - a^(4) * A * b^(4) * B^(2) * C^(2) - a^(2) * A * b^(6) * B^(2) * C^(2) + A * b^(8) * B^(2) * C^(2) + 2 * a^(8) * B^(3) * C^(2) - 4 * a^(6) * b^(2) * B^(3) * C^(2) + 2 * a^(4) * b^(4) * B^(3) * C^(2) + 2 * a^(6) * A^(2) * B * c^(2) * C^(2) - 3 * a^(4) * A^(2) * b^(2) * B * c^(2) * C^(2) + A^(2) * b^(6) * B * c^(2) * C^(2) - a^(6) * A * B^(2) * c^(2) * C^(2) + 3 * a^(2) * A * b^(4) * B^(2) * c^(2) * C^(2) - 2 * A * b^(6) * B^(2) * c^(2) * C^(2) + 2 * A^(3) * b^(4) * c^(4) * C^(2) + 3 * a^(2) * A^(2) * b^(2) * B * c^(4) * C^(2) - A^(2) * b^(4) * B * c^(4) * C^(2) + a^(4) * A * B^(2) * c^(4) * C^(2) - 3 * a^(2) * A * b^(2) * B^(2) * c^(4) * C^(2) - 2 * a^(4) * B^(3) * c^(4) * C^(2) - 2 * a^(2) * A^(2) * B * c^(6) * C^(2) - A^(2) * b^(2) * B * c^(6) * C^(2) + a^(2) * A * B^(2) * c^(6) * C^(2) + 2 * A * b^(2) * B^(2) * c^(6) * C^(2) + A^(2) * B * c^(8) * C^(2) - A * B^(2) * c^(8) * C^(2) - 2 * a^(4) * A^(2) * b^(4) * C^(3) + 2 * A^(2) * b^(8) * C^(3) - a^(8) * A * B * C^(3) - 2 * a^(6) * A * b^(2) * B * C^(3) + 2 * a^(2) * A * b^(6) * B * C^(3) + A * b^(8) * B * C^(3) - 2 * a^(8) * B^(2) * C^(3) + 2 * a^(4) * b^(4) * B^(2) * C^(3) - 4 * A^(2) * b^(6) * c^(2) * C^(3) + 3 * a^(6) * A * B * c^(2) * C^(3) + 3 * a^(4) * A * b^(2) * B * c^(2) * C^(3) - 3 * a^(2) * A * b^(4) * B * c^(2) * C^(3) - 3 * A * b^(6) * B * c^(2) * C^(3) + 4 * a^(6) * B^(2) * c^(2) * C^(3) + 2 * A^(2) * b^(4) * c^(4) * C^(3) - 3 * a^(4) * A * B * c^(4) * C^(3) + 3 * A * b^(4) * B * c^(4) * C^(3) - 2 * a^(4) * B^(2) * c^(4) * C^(3) + a^(2) * A * B * c^(6) * C^(3) - A * b^(2) * B * c^(6) * C^(3) = 0)
P = Point(f)
polígono2, D, E, F = TrianguloPedal(L, M, N, P)
d = ortotransversal(L, M, N, P)
e = ortotransversal(D, E, F, P)
G = Intersect(d, e)
X_{1114} = TriangleCenter(L, M, N, 1114)
X_{1113} = TriangleCenter(L, M, N, 1113)
X_3 = TriangleCenter(L, M, N, 3)
X_4 = TriangleCenter(L, M, N, 4)
g = Circle(L, M, N)
polígono3, H_a, H_b, H_c = TrianguloPedal(L, M, N, X_4)
h = Line(L, X_4)
i = Line(M, X_4)
j = Line(N, X_4)
k = Line(X_4, X_3)
M_a = Midpoint(a)
M_b = Midpoint(b)
M_c = Midpoint(c)
p = Circle(M_a, M)
q = Circle(M_b, L)
r = Circle(M_c, L)
l = Line(L, X_3)
m = Line(M, X_3)
n = Line(N, X_3)
A_1, A_2 = Intersect(p, l)
B_1, B_2 = Intersect(q, m)
C_1, C_2 = Intersect(r, n)
s = ortotransversal(L, M, N, A_2)
a_1 = ortotransversal(L, M, N, A_1)
o = Cubic(L, M, N, 6)

Tool: TrianguloETC
Dar el vértice A
Input: A_{etc}
Output: B_{etc}, C_{etc}, a, polígono1

c = Circle(A_{etc}, 13)
B_{etc} = Point(c)
d = Circle(A_{etc}, 9)
e = Circle(B_{etc}, 6)
C_{etc} = Intersect(d, e, 1)
polígono1, c_{etc}, a_{etc}, b_{etc} = Polygon(A_{etc}, B_{etc}, C_{etc})
a = Line(B_{etc}, C_{etc})

Tool: Coordenadas Trilineales (command CoordenadasTrilineales)
Dar los vértices de ABC y un  punto P
Input: A, B, C, P
Output: texto2, CoordTrilineales

q_1 = Segment(B, P)
e = Line(A, C)
E_1 = Intersect(e, q_1)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
ABC, c, a, b = Polygon(A, B, C)
e_1 = OrthogonalLine(P, a)
D = Intersect(e_1, d)
p = Segment(P, D)
α = If(Defined[D_1], -p, p)
f_1 = OrthogonalLine(P, b)
g = OrthogonalLine(P, c)
f = Line(A, B)
E = Intersect(f_1, e)
F = Intersect(g, f)
r_1 = Segment(P, C)
q = Segment(P, E)
r = Segment(P, F)
F_1 = Intersect(f, r_1)
β = If(Defined[E_1], -q, q)
γ = If(Defined[F_1], -r, r)
CoordTrilineales: {α, β, γ}
texto2: "" + CoordTrilineales + ""

Tool: Triangulo Pedal (command TrianguloPedal)
Dar ABC y P
Input: A, B, C, E
Output: polígono2, F, G, H

polígono1, c, a, b = Polygon(A, B, C)
e = OrthogonalLine(E, a)
f = OrthogonalLine(E, b)
g = OrthogonalLine(E, c)
h = Line(B, C)
i = Line(C, A)
j = Line(A, B)
F = Intersect(e, h)
G = Intersect(i, f)
H = Intersect(j, g)
polígono2, h_1, f_1, g_1 = Polygon(F, G, H)

Tool: ortotransversal
DAr ABC y P, construye la recta ortotransversal de P
Input: A, B, C, P
Output: m

e = Segment(P, B)
f = Segment(P, C)
h = OrthogonalLine(P, e)
i = OrthogonalLine(P, f)
k = Line(C, A)
l = Line(A, B)
E = Intersect(h, k)
F = Intersect(i, l)
m = Line(F, E)

Tool: Tripolar
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: l

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
E = Intersect(h, e)
F = Intersect(d, g)
j = Line(E, F)
G = Intersect(f, i)
k = Line(G, F)
H = Intersect(e, k)
I = Intersect(j, f)
l = Line(H, 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: rectaEuler
Dar los vértices de un triángulo
Input: D, E, F
Output: m

G = TriangleCenter(D, E, F, 4)
H = TriangleCenter(D, E, F, 3)
m = Line(H, G)