Cúbica K018 y triángulos perspectivos
Author: Angel Montesdeoca
Date: 11 Junio 2015

A = (-3.05742232931882, -0.04921866215703217)
B = (14.598801040929665, -0.5264138883799668)
C = (10.470850232185041, 7.772664898543952)
K018 = Cubic(A, B, C, 18)
polígono1, c, a, b = Polygon(A, B, C)
F = Midpoint(c)
E = Midpoint(b)
D = Midpoint(a)
q = Circle(D, E, F)
d = Circle(D, C)
M = Point(d)
P = Point(K018)
p = Circle(P, D, M)
G = Center(p)
g = Circle(P, D, B)
H = Center(g)
h = Segment(H, D)
B'_1 = Mirror(B, h)
i = Line(B'_1, B)
f = Segment(D, G)
j = OrthogonalLine(M, f)
B' = PuntoFijoEjesRadicales(B, C, A, P)
C' = PuntoFijoEjesRadicales(C, A, B, P)
m = Line(B', B)
n = Line(C', C)
e = Line(P, D)
A' = Intersect(i, e)
polígono2, c', a', b' = Polygon(A', B', C')
k = Line(A', A)
Q = Intersect(n, m)
X_2 = TriangleCenter(A, B, C, 2)
X_{13} = TriangleCenter(A, B, C, 13)
X_{14} = TriangleCenter(A, B, C, 14)
X_6 = TriangleCenter(A, B, C, 6)
X_{15} = TriangleCenter(A, B, C, 15)
X_{16} = TriangleCenter(A, B, C, 16)
X_{111} = TriangleCenter(A, B, C, 111)

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: EjeRadical
Dar centro, punto y centro, punto
Input: A, B, C, D
Output: i

e = Circle(B, D, A)
E = Center(e)
a = Segment(A, E)
b = Segment(E, C)
B' = Mirror(B, a)
D' = Mirror(D, b)
f = Segment(A, C)
g = Line(B, B')
h = Line(D', D)
F = Intersect(g, h)
i = OrthogonalLine(F, f)

Tool: Punto Fijo Ejes Radicales (command PuntoFijoEjesRadicales)
Dar ABC y P
Input: A, B, C, P
Output: A'

polígono1, c, a, b = Polygon(A, B, C)
D = Midpoint(a)
e = Line(P, D)
g = Circle(P, D, B)
H = Center(g)
h = Segment(H, D)
B' = Mirror(B, h)
i = Line(B', B)
A' = Intersect(e, i)