Author: Angel Montesdeoca
Date: 29 Octubre 2015

A

B

C

$\mathcal{C}(P)$

Recta Pascal

$\mathcal C_A$

$\mathcal C_B$

$\mathcal C_C$

Punto en D en C_A

Cónicas C_B y C_c

L = (-2.273626273404998, 2.7342308554351256)
M = (15.982101477602757, 2.73959251358936)
N = (9.590318632830934, 13.82534430341185)
X_2 = TriangleCenter(L, M, N, 2)
C' = Mirror(N, X_2)
B' = Mirror(M, X_2)
e_1 = Conic(M, N, L, B', C')
o = TriangleCurve(L, M, N, 3 * A^(4) * B^(2) + 6 * A^(3) * B^(3) + 3 * A^(2) * B^(4) + 2 * A^(4) * B * C + 2 * A * B^(4) * C + 3 * A^(4) * C^(2) - 42 * A^(2) * B^(2) * C^(2) + 3 * B^(4) * C^(2) + 6 * A^(3) * C^(3) + 6 * B^(3) * C^(3) + 3 * A^(2) * C^(4) + 2 * A * B * C^(4) + 3 * B^(2) * C^(4) = 0)
polígono1, c, a, b = Polygon(L, M, N)
P = Point(o)
d_2, P_0 = ConicaCircunscrita(L, M, N, P)
u = Vector(L, P)
e = Line(N, M)
t_A = Tangent(L, d_2)
h = Line(L, P)
l = Line(N, u)
g = LineBisector(M, N)
i = AngularBisector(M, L, N)
A'_1 = Intersect(i, g)
d = Line(M, A'_1)
A_1 = Intersect(t_A, e)
B_1 = Intersect(h, d)
m = Line(B_1, A_1)
C_1 = Intersect(m, l)
n = Line(L, C_1)
D = Intersect(n, d)
C_A, F = IPPPP(u, L, M, N, D)
A_P = Center(C_A)
f, B_P = ConicaC_a(M, N, L, P)
k, C_P = ConicaC_a(N, L, M, P)
p = false
q = false
r = Line(A_P, B_P)
H_{a1} = Trilinear(L, M, N, c, 0, a - sqrt(13) * a)
s = Line(H_{a1}, a)
H_{a2} = Trilinear(L, M, N, c, 0, a + sqrt(13) * a)
t = Line(H_{a2}, a)
a_1 = Line(Trilinear[L, M, N, b - sqrt(13) * b, a, 0], Line[N, L])
b_1 = Line(Trilinear[L, M, N, b + sqrt(13) * b, a, 0], Line[N, L])
c_1 = Line(Trilinear[L, M, N, 0, c - sqrt(13) * c, b], Line[L, M])
d_1 = Line(Trilinear[L, M, N, 0, c + sqrt(13) * c, b], Line[L, M])
A' = Mirror(L, X_2)
j = Tangent(A', e_1)
A'' = Dilate(L, 4, X_2)
B'' = Dilate(M, 4, X_2)
C'' = Dilate(N, 4, X_2)
f_1 = Dilate(e_1, 4, X_2)

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: cociente ceviano (command cocienteceviano)
Input: A, B, C, P, Q
Output: P_Q

d = Line(A, B)
e = Line(B, C)
f = Line(A, C)
g = Line(Q, C)
h = Line(Q, B)
i = Line(Q, A)
D = Intersect(i, e)
E = Intersect(h, f)
F = Intersect(g, d)
j = Line(E, D)
l = Line(F, E)
n = Line(F, D)
I = Intersect(f, n)
p = Line(I, B)
G = Intersect(d, j)
k = Line(C, G)
H = Intersect(e, l)
m = Line(A, H)
J = Intersect(k, p)
K = Intersect(k, m)
q = Line(P, A)
r = Line(B, P)
N = Intersect(f, r)
O = Intersect(q, e)
t = Line(O, J)
a_1 = Line(N, K)
P_Q = Intersect(a_1, t)

Tool: Conica Circunscrita (command ConicaCircunscrita)
Dar ABC y el perspector P
Input: A, B, C, P
Output: d, Q

X_2 = TriangleCenter(A, B, C, 2)
Q = cocienteceviano(A, B, C, X_2, P)
B' = Mirror(B, Q)
C' = Mirror(C, Q)
d = Conic(A, B, C, B', C')

Tool: Coordenadas Baricentrias (command CoordenadasBaricentrias)
Dar los vértices ABC y un punto P
Input: A, B, C, P
Output: texto2, CoordBaricentricas

q_1 = Segment(B, P)
APB, b_2, a_2, p_4 = Polygon(A, P, B)
e = Line(A, C)
E_1 = Intersect(e, q_1)
CPA, a_1, c_2, p_3 = Polygon(C, P, A)
BPC, c_1, b_1, p_2 = Polygon(B, P, C)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
f = Line(A, B)
r_1 = Segment(P, C)
F_1 = Intersect(f, r_1)
xx = If(Defined[D_1], -BPC, BPC)
yy = If(Defined[E_1], -CPA, CPA)
zz = If(Defined[F_1], -APB, APB)
CoordBaricentricas: {xx, yy, zz}
texto2: "" + CoordBaricentricas + ""

Tool: IPPPP
Conica dada la dirección de un punto del infinto y cuatro puntos más
Input: u, P_1, P_2, P_3, P_4
Output: h, X

a = Line(P_4, u)
M = Point(a)
b = Line(P_1, M)
d = Line(P_1, P_2)
V = Intersect(a, d)
c = Line(P_3, P_4)
U = Intersect(b, c)
e = Line(V, U)
f = Line(P_2, P_3)
W = Intersect(e, f)
g = Line(W, u)
X = Intersect(b, g)
h = Conic(P_1, P_2, P_3, P_4, X)

Tool: Conica C_a (command ConicaC_a)
Dar ABC y un punto P
Input: L, M, N, P
Output: p, A_P

C

B

A

Recta Pascal

IPPt_p

d, D = ConicaCircunscrita(L, M, N, P)
u = Vector(L, P)
e = Line(N, M)
t_A = Tangent(L, d)
h = Line(L, P)
l = Line(N, u)
g = LineBisector(M, N)
i = AngularBisector(M, L, N)
A' = Intersect(i, g)
j = Line(M, A')
A_1 = Intersect(t_A, e)
B_1 = Intersect(h, j)
m = Line(B_1, A_1)
C_1 = Intersect(m, l)
n = Line(L, C_1)
E = Intersect(n, j)
p, F = IPPPP(u, L, M, N, E)
A_P = Center(p)