Euler line

Euler line of A'B'C'

Kiepert parabola of A'B'C'

Kiepert parabola

A = (-3.469689140262145, -1.5428019476100756)
B = (9.74927081839549, -1.6263582903663396)
C = (4.756538990032686, 6.709623154987494)
polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(A, a)
e = OrthogonalLine(B, b)
f = OrthogonalLine(C, c)
X_4 = TriangleCenter(A, B, C, 4)
polígono2, D, E, F = TrianguloCeviano(A, B, C, X_4)
C_a = Mirror(C, d)
C_b = Mirror(C, e)
B_a = Mirror(B, d)
B_c = Mirror(B, f)
A_c = Mirror(A, f)
A_b = Mirror(A, e)
g = Line(B_a, A_b)
h = Line(A_c, C_a)
i = Line(C_b, B_c)
A' = Intersect(g, h)
B' = Intersect(g, i)
C' = Intersect(i, h)
polígono3, c', a', b' = Polygon(A', B', C')
X_{110} = TriangleCenter(A, B, C, 110)
k = Circle(A, B, C)
p = Circle(A', C', B')
X_3 = Center(k)
O' = Center(p)
j = Line(O', X_3)
X_{107} = TriangleCenter(A, B, C, 107)
l = Line(X_3, X_4)
H' = TriangleCenter(A', B', C', 4)
m = Line(O', H')
q = Parabola(X_{110}, m)
r = Parabola(X_{110}, l)
X_{94} = TriangleCenter(A, B, C, 94)
X_{143} = TriangleCenter(A, B, C, 143)

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: Afinidad
Dado ABC, A'B'C' y X, determiana el punto fijo propio y la imagen de X
Input: A, B, C, A', B', C', X
Output: F, X'

polígono1, c, a, b = Polygon(A, B, C)
polígono2, f, d, e = Polygon(A', B', C')
g = Line(A, a)
h = Line(C, c)
i = Line(A', d)
j = Line(C', f)
k = Line(A, B)
l = Line(A', B')
L = Intersect(k, l)
m = Line(B, C)
n = Line(B', C')
M = Intersect(m, n)
N = Intersect(j, h)
P = Intersect(g, i)
p = Line(L, N)
q = Line(M, P)
F = Intersect(p, q)
r = Line(X, c)
U = Intersect(p, r)
s = Line(X, g)
V = Intersect(q, s)
t = Line(U, f)
a_1 = Line(V, i)
X' = Intersect(a_1, t)

Tool: Afinidad Rectas Fijas (command AfinidadRectasFijas)
Dar ABC y A'B'C' determinas las rectas dobles (si existen) de la afinidad
Input: C, B, A, A', B', C'
Output: t, s

h = AngularBisector(B, A, C)
g = Circle(A, B, C)
P = Point(g)
i = Line(A, P)
i' = Mirror(i, h)
Ma = Point(i')
F, M'a = Afinidad(A, B, C, A', B', C', Ma)
k = Line(A, C)
l = Line(A', C')
E = Intersect(l, k)
m = Line(A, B)
n = Line(A', B')
G = Intersect(n, m)
p = Conic(A, A', F, E, G)
q, r = Asymptote(p)
s = Line(F, q)
t = Line(F, r)

Tool: Herramienta6
Input: A, B, C
Output: K

polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(A, a)
e = OrthogonalLine(B, b)
f = OrthogonalLine(C, c)
C_a = Mirror(C, d)
C_b = Mirror(C, e)
B_a = Mirror(B, d)
B_c = Mirror(B, f)
A_c = Mirror(A, f)
A_b = Mirror(A, e)
g = Line(B_a, A_b)
h = Line(A_c, C_a)
i = Line(C_b, B_c)
A' = Intersect(g, h)
B' = Intersect(g, i)
C' = Intersect(i, h)
p = Circle(A', C', B')
K = Center(p)