Euler A_1A_2A_3

Euler B_1B_2B_3

Euler C_1C_2C_3

\shadowbox{X_{74}W : WX_{1986} = 3}

A = (4.122502166983389, 19.31501675390904)
B = (-3.05742232931882, -1.2899262503366624)
C = (22.901997977208683, -1.0990481598474884)
polígono1, c, a, b = Polygon(A, B, C)
X_4 = TriangleCenter(A, B, C, 4)
polígono2, A_a, B_b, C_c = TrianguloPedal(A, B, C, X_4)
d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = OrthogonalLine(A_a, e)
A_b = Intersect(e, g)
h = OrthogonalLine(A_a, f)
A_c = Intersect(h, f)
polígono3, a_c, a_a, a_b = Polygon(A_a, A_b, A_c)
polígono4, B_c, B_a = A_ortiaco(B, C, A)
polígono5, C_a, C_b = A_ortiaco(C, A, B)
X_6 = TriangleCenter(A, B, C, 6)
X_{74} = TriangleCenter(A, B, C, 74)
k = Circle(A, B, C)
i = Line(X_6, X_{74})
X_{1986} = TriangleCenter(A, B, C, 1986)
A_1 = Midpoint(A_a, A)
A_2 = Midpoint(A_a, A_b)
A_3 = Midpoint(A_a, A_c)
polígono6, c_1, a_1, b_1 = Polygon(A_1, A_2, A_3)
B_1 = Midpoint(B_b, B)
B_2 = Midpoint(B_b, B_a)
B_3 = Midpoint(B_b, B_c)
polígono7, b_3, b_2, b_4 = Polygon(B_1, B_2, B_3)
C_1 = Midpoint(C_c, C)
C_2 = Midpoint(C_c, C_a)
C_3 = Midpoint(C_c, C_b)
polígono8, c_3, c_2, c_4 = Polygon(C_1, C_2, C_3)
j = rectaEuler(A_1, A_2, A_3)
l = rectaEuler(B_1, B_2, B_3)
m = rectaEuler(C_1, C_3, C_2)
W = Intersect(l, m)
n = Line(A_a, j)
p = Line(B_b, l)
q = Line(C_c, m)
r = Line(A, j)
s = Line(B, l)
t = Line(C, m)
D = Midpoint(X_{74}, X_{1986})
E = Midpoint(X_{74}, D)

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: A_ortiaco
Dar ABC, construye el ortíaco relativo a A.
Input: A, B, C
Output: polígono3, A_b, A_c

X_4 = TriangleCenter(A, B, C, 4)
polígono2, A_a, B_b, C_c = TrianguloPedal(A, B, C, X_4)
e = Line(C, A)
f = Line(A, B)
g = OrthogonalLine(A_a, e)
A_b = Intersect(e, g)
h = OrthogonalLine(A_a, f)
A_c = Intersect(h, f)
polígono3, a_c, a_a, a_b = Polygon(A_a, A_b, A_c)

Tool: puntoRazon
Punto X que divide al segmento de extremos P y Q, según una razón  dada, PX : XQ = m : n
Input: P, Q, m, n
Output: X

X = Dilate(Q, m / (m + n), P)

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)