C

B

A

orthotransversal of P wrt ABC

orthotransversal of P wrt P_aP_bP_c

trilinear polar of P

Euler line

Q003

N = (21.172720723181946, 23.141436594199227)
M = (38.995502332240775, -9.412419610102274)
L = (-11.033391351763896, -6.076372396059949)
polígono1, c, a, b = Polygon(L, M, N)
o = TriangleCurve(L, M, N, a^(2) * A^(3) * B^(2) * c^(2) - A^(3) * b^(2) * B^(2) * c^(2) + a^(2) * A^(2) * B^(3) * c^(2) - A^(2) * b^(2) * B^(3) * c^(2) - A^(3) * B^(2) * c^(4) + A^(2) * B^(3) * c^(4) - a^(2) * A^(3) * b^(2) * C^(2) + A^(3) * b^(4) * C^(2) - a^(4) * B^(3) * C^(2) + a^(2) * b^(2) * B^(3) * C^(2) + A^(3) * b^(2) * c^(2) * C^(2) - a^(2) * B^(3) * c^(2) * C^(2) - a^(2) * A^(2) * b^(2) * C^(3) - A^(2) * b^(4) * C^(3) + a^(4) * B^(2) * C^(3) + a^(2) * b^(2) * B^(2) * C^(3) + A^(2) * b^(2) * c^(2) * C^(3) - a^(2) * B^(2) * c^(2) * C^(3) = 0)
X_1 = TriangleCenter(L, M, N, 1)
X_2 = TriangleCenter(L, M, N, 2)
X_4 = TriangleCenter(L, M, N, 4)
X_{13} = TriangleCenter(L, M, N, 13)
X_{14} = TriangleCenter(L, M, N, 14)
X_{357} = TriangleCenter(L, M, N, 357)
X_{1113} = TriangleCenter(L, M, N, 1113)
X_{1114} = TriangleCenter(L, M, N, 1114)
t = Circle(L, M, N)
X_{1134} = TriangleCenter(L, M, N, 1134)
X_{1136} = TriangleCenter(L, M, N, 1136)
X_{1156} = TriangleCenter(L, M, N, 1156)
I_a = Trilinear(L, M, N, -1, 1, 1)
I_b = Trilinear(L, M, N, -1, 1, -1)
I_c = Trilinear(L, M, N, 1, 1, -1)
P = Point(o)
polígono2, P_a, P_b, P_c = TrianguloCeviano(L, M, N, P)
g = ortotransversal(L, M, N, P)
h = ortotransversal(P_a, P_b, P_c, P)
i = Tripolar(L, M, N, P)
polígono3, H_a, H_b, H_c = TrianguloCeviano(L, M, N, X_4)
j = Line(X_2, X_4)
k = Line(L, X_4)
l = Line(X_4, M)
m = Line(X_4, N)

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 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: 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: 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)