(e) Euler line

(H_M)

Neuberg cubic

A = (-0.92, -1.02)
B = (8.18, -1.02)
C = (5.785301694211941, 4.59327197457865)
polígono1, c, a, b = Polygon(A, B, C)
X_3 = TriangleCenter(A, B, C, 3)
X_4 = TriangleCenter(A, B, C, 4)
d_1 = Line(X_3, X_4)
M = Point(d_1)
M' = Mirror(X_3, M)
e = Conic(A, B, C, X_4, M)
X_{399} = TriangleCenter(A, B, C, 399)
d = Line(X_{399}, M')
P, Q = Intersect(e, d)
K001 = Cubic(A, B, C, 1)
p_a = rectaEuler(P, B, C)
p_b = rectaEuler(P, C, A)
p_c = rectaEuler(P, A, B)
i = OrthogonalLine(C, p_b)
j = OrthogonalLine(B, p_c)
q_a = rectaEuler(B, C, Q)
q_b = rectaEuler(C, A, Q)
q_c = rectaEuler(A, B, Q)

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: 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)