Q_i*

co(P,Q_i)

Q_i

perspector of co(P,Q_i)

trilinear polar of P

A = (-9.186283387198575, 4.295664793447468)
B = (22.600478135042227, 3.081872803024187)
C = (18.556870618770226, 19.561631829323964)
d = Circle(A, B, C)
Q' = Point(d)
polígono1, c, a, b = Polygon(A, B, C)
P = (17.917368501226676, 10.983047370645233)
e = AngularBisector(B, A, C)
Q'' = Mirror(Q', e)
u = Vector(A, Q'')
f = LineBisector(Q'', A)
M = Point(f)
δ = OrthogonalLine(M, f)
h = Line(A, B)
i = Line(A, C)
D_b = Intersect(δ, i)
D_c = Intersect(h, δ)
g = Segment(B, P)
j = Segment(C, P)
k = Line(D_b, j)
l = Line(D_c, g)
A' = Intersect(k, l)
m = Line(P, A')
D = Intersect(δ, m)
p, E = IPPPP(u, A, B, C, P)
F = PerspectorConica(A, B, C, p)
n = Tripolar(A, B, C, P)
q, r = Asymptote(p)
v = Vector(A, A')

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: 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: Perspector Conica (command PerspectorConica)
Dar ABC y una cónica (no necesariamente circunscrita)
Input: A, B, C, d
Output: L

e = Polar(A, d)
f = Polar(B, d)
g = Polar(C, d)
I = Intersect(e, g)
h = Line(B, I)
J = Intersect(e, f)
i = Line(C, J)
L = Intersect(i, h)

Tool: Tripolar
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: l

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
E = Intersect(h, e)
F = Intersect(d, g)
j = Line(E, F)
G = Intersect(f, i)
k = Line(G, F)
H = Intersect(e, k)
I = Intersect(j, f)
l = Line(H, I)

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')