$\Psi$

$P^\bullet$

$H(M,\Psi)$

$\Phi$

Mostar Par Bicéntrico

  \text{Mostrar/Ocultar} \textcolor{red}{X_{468}}\
\text{como punto medio del }\
\text{par bicéntrico} P(4), U(4).\
ABC \text{ \textcolor{red}{no} puede ser acutángulo}

Lugar geométrico de los centros N de las
hipérbolas de Apolonio relativas a M (punto
variabe sobre la circunferencia circunscrita) 
y a la cónica inscrita de centro en el simediano.

B_a

B_a es el punto de intersección 
del diámetro por B con la perpendicular 
trazada desde M a su diámetro conjugado

 ¡¡El triángulo ABC no
puede ser acutángulo!!

Euler  line

Orthic axis

C = (14.272863675370512, 15.32155766540306)
B = (20.179664935687406, 2.5926231810241003)
A = (-0.18623267362603535, 2.215476928999773)
X_4 = TriangleCenter(A, B, C, 4)
polígono1, c, a, b = Polygon(A, B, C)
P: X_4
d = ConicaInscrita(A, B, C, P)
e = Circle(A, B, C)
M = Point(e)
D = ConjugadoIsotomico(A, B, C, P)
X_2 = TriangleCenter(A, B, C, 2)
E = Midpoint(D, X_2)
X_6 = Mirror(E, X_2)
f = Line(B, X_6)
g = Diameter(f, d)
h = OrthogonalLine(M, g)
B_a = Intersect(f, h)
i = OrthogonalLine(M, f)
B'_a = Intersect(g, i)
j = Line(C, X_6)
k = Diameter(j, d)
l_1 = OrthogonalLine(M, k)
C_a = Intersect(j, l_1)
m = OrthogonalLine(M, j)
C'_a = Intersect(k, m)
p = Conic(B_a, C'_a, B'_a, C_a, M)
N = Center(p)
lugar1 = Locus(N, M)
X_{468} = TriangleCenter(A, B, C, 468)
X_3 = TriangleCenter(A, B, C, 3)
X_{125} = TriangleCenter(A, B, C, 125)
F, G, H, I = Vertex(d)
n = Segment(F, G)
q = Segment(I, H)
r = Line(X_{125}, n)
J = Mirror(X_{468}, X_{125})
K = Mirror(X_{468}, r)
O = Midpoint(a)
Q = Midpoint(b)
R = Midpoint(c)
c_1 = Circle(O, Q, R)
X_5 = TriangleCenter(A, B, C, 5)
a_1 = Segment(X_5, X_3)
b_1 = OrthogonalLine(X_{468}, a_1)
K' = Mirror(K, X_{125})
Lg = Conic(X_{468}, K, K', J, N)
U4, P4 = Intersect(e, b_1)
P4U4 = true
o = Segment(U4, P4)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
Ba = false
L, S, T, U = Vertex(Lg)
l = Segment(L, S)
s = Segment(T, U)
t = Line(X_4, X_3)
X_{25} = TriangleCenter(A, B, C, 25)
X_{297} = TriangleCenter(A, B, C, 297)
d_1 = OrthogonalLine(X_{297}, t)
X_{1113} = TriangleCenter(A, B, C, 1113)
X_{1114} = TriangleCenter(A, B, C, 1114)

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: Conjugado Isotomico (command ConjugadoIsotomico)
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: D

$P^\bullet$

polígono1, c, a, b = Polygon(A, B, C)
E = Midpoint(b)
F = Midpoint(c)
g = Line(C, A)
h = Line(A, B)
j = Line(P, B)
k = Line(P, C)
I = Intersect(g, j)
J = Intersect(h, k)
J' = Mirror(J, F)
m = Line(C, J')
I' = Mirror(I, E)
d = Line(B, I')
D = Intersect(m, d)

Tool: ConicaInscrita
Dar ABC y su perspector P
Input: A, B, C, P
Output: k

$P^\bullet$

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(A, P)
h = Line(P, B)
i = Line(P, C)
D = Intersect(g, d)
E = Intersect(e, h)
F = Intersect(f, i)
G = ConjugadoIsotomico(A, B, C, P)
X_2 = TriangleCenter(A, B, C, 2)
H = Midpoint(X_2, G)
Q = Mirror(H, X_2)
F' = Mirror(F, Q)
E' = Mirror(E, Q)
k = Conic(D, E, F, E', F')