Circunferencias de Apolonio

$\Gamma_a$

$\Gamma_a$

$\Gamma_c$

X_{39}

$\Gamma_e$

$\Gamma_i$

$\Gamma_{ai}$

$\Gamma_{bi}$

$\Gamma_{ci}$

$\Gamma_{ae}$

$\Gamma_{be}$

$\Gamma_{ce}$

Brocard axis

X_{1343}

X_{1342}

X_{39} radical c.

T_e

T_i

W_i

W_e

Radical center

V_e

V_i

O_e=X_{8160}

O_i=X_{8161}

R_e

R_i

X_{8161}

↑ Points on 
Brocart axis

X_{8160}

A = (-3.757810672139072, -0.7284209022830949)
B = (37.870879840116764, -1.3313219405672492)
C = (26.318116461431718, 25.282622283242087)
polígono1, c, a, b = Polygon(A, B, C)
X_3 = TriangleCenter(A, B, C, 3)
X_6 = TriangleCenter(A, B, C, 6)
B_a = Intersect(Line[A, C], Line[Intersect[Line[B, C], Line[A, X_6]], Line[A, B]])
C_a = Intersect(Line[A, B], Line[Intersect[Line[B, C], Line[A, X_6]], Line[A, C]])
C_b = Intersect(Line[B, A], Line[Intersect[Line[C, A], Line[B, X_6]], Line[B, C]])
A_c = Intersect(Line[C, B], Line[Intersect[Line[A, B], Line[C, X_6]], Line[C, A]])
A_b = Intersect(Line[B, C], Line[Intersect[Line[C, A], Line[B, X_6]], Line[B, A]])
B_c = Intersect(Line[C, A], Line[Intersect[Line[A, B], Line[C, X_6]], Line[C, B]])
g_a = Circle(B, C, B_a)
g_b = Circle(C, A, C_b)
g_c = Circle(A, B, A_c)
O_a = Center(g_a)
O_b = Center(g_b)
O_c = Center(g_c)
R = Intersect(EjeRadical[O_a, B, O_b, C], EjeRadical[O_a, B, O_c, A])
E_a = Intersect(Line[B, C], Line[O_b, O_c])
E_b = Intersect(Line[C, A], Line[O_c, O_a])
E_c = Intersect(Line[A, B], Line[O_a, O_b])
I_a = Intersect(Line[A, X_3], Line[O_b, O_c])
I_b = Intersect(Line[B, X_3], Line[O_c, O_a])
I_c = Intersect(Line[C, X_3], Line[O_a, O_b])
A_e = Intersect(g_a, Ray[R, Intersect[Line[B, C], Line[A, X_6]]])
B_e = Intersect(g_b, Ray[R, Intersect[Line[C, A], Line[B, X_6]]])
C_e = Intersect(g_c, Ray[R, Intersect[Line[A, B], Line[C, X_6]]])
g_e = Circle(A_e, B_e, C_e)
O_e = Center(g_e)
P_{aa} = Intersect(Polar[I_b, g_a], Polar[I_c, g_a])
A_i = Intersect(g_a, Ray[R, P_{aa}])
P_{bb} = Intersect(Polar[I_c, g_b], Polar[I_a, g_b])
B_i = Intersect(g_b, Ray[R, P_{bb}])
P_{cc} = Intersect(Polar[I_a, g_c], Polar[I_b, g_c])
C_i = Intersect(g_c, Ray[R, P_{cc}])
g_i = Circle(A_i, B_i, C_i)
O_i = Center(g_i)
P_{ab} = Intersect(Polar[I_b, g_b], Polar[I_c, g_b])
A_{be} = Intersect(g_b, Ray[R, P_{ab}])
P_{ac} = Intersect(Polar[I_b, g_c], Polar[I_c, g_c])
A_{ce} = Intersect(g_c, Ray[R, P_{ac}])
g_{ai} = Circle(A_e, A_{be}, A_{ce})
O_{ai} = Center(g_{ai})
P_{ba} = Intersect(Polar[I_c, g_a], Polar[I_a, g_a])
B_{ae} = Intersect(g_a, Ray[R, P_{ba}])
P_{bc} = Intersect(Polar[I_c, g_c], Polar[I_a, g_c])
B_{ce} = Intersect(g_c, Ray[R, P_{bc}])
g_{bi} = Circle(B_e, B_{ce}, B_{ae})
O_{bi} = Center(g_{bi})
P_{cb} = Intersect(Polar[I_a, g_b], Polar[I_b, g_b])
C_{be} = Intersect(g_b, Ray[R, P_{cb}])
P_{ca} = Intersect(Polar[I_a, g_a], Polar[I_b, g_a])
C_{ae} = Intersect(g_a, Ray[R, P_{ca}])
g_{ci} = Circle(C_e, C_{ae}, C_{be})
O_{ci} = Center(g_{ci})
A_{bi} = Intersect(g_b, Ray[R, Vector[P_{ab}, R]])
A_{ci} = Intersect(g_c, Ray[R, Vector[P_{ac}, R]])
g_{ae} = Circle(A_i, A_{bi}, A_{ci})
O_{ae} = Center(g_{ae})
B_{ai} = Intersect(g_a, Ray[R, Vector[P_{ba}, R]])
B_{ci} = Intersect(g_c, Ray[R, Vector[P_{bc}, R]])
g_{be} = Circle(B_i, B_{ci}, B_{ai})
O_{be} = Center(g_{be})
C_{bi} = Intersect(g_b, Ray[R, Vector[P_{cb}, R]])
C_{ai} = Intersect(g_a, Ray[R, Vector[P_{ca}, R]])
g_{ce} = Circle(C_i, C_{ai}, C_{bi})
O_{ce} = Center(g_{ce})
d = Line(A, O_{ae})
e = Line(B, O_{be})
f = Line(C, O_{ce})
g = Line(X_3, X_6)
T_e = Intersect(e, f)
h = Line(A, O_{ai})
i = Line(B, O_{bi})
j = Line(C, O_{ci})
T_i = Intersect(j, i)
k = Line(A_{ce}, A_{be})
l = Line(B_{ae}, B_{ce})
m = Line(C_{be}, C_{ae})
A' = Intersect(l, m)
B' = Intersect(k, m)
C' = Intersect(k, l)
n = Line(C', C)
p = Line(B', B)
q = Line(A', A)
W_i = Intersect(n, p)
r = Line(A_{bi}, A_{ci})
s = Line(B_{ai}, B_{ci})
t = Line(C_{bi}, C_{ai})
A'' = Intersect(s, t)
B'' = Intersect(t, r)
C'' = Intersect(r, s)
a_1 = Line(A'', A)
b_1 = Line(B, B'')
c_1 = Line(C, C'')
W_e = Intersect(c_1, b_1)
d_1 = Line(B_{ae}, C_{ae})
e_1 = Line(C_{be}, A_{be})
f_1 = Line(A_{ce}, B_{ce})
A''' = Intersect(e_1, f_1)
B''' = Intersect(d_1, f_1)
C''' = Intersect(d_1, e_1)
g_1 = Line(A''', A)
h_1 = Line(B, B''')
i_1 = Line(C, C''')
j_1 = Line(O_{ae}, O_{ai})
k_1 = Line(O_{be}, O_{bi})
l_1 = Line(O_{ci}, O_{ce})
m_1 = Line(A_e, A)
n_1 = Line(B_e, B)
p_1 = Line(C_e, C)
X_{1343} = TriangleCenter(A, B, C, 1343)
X_{1342} = TriangleCenter(A, B, C, 1342)
q_1 = Line(A, A_i)
r_1 = Line(B, B_i)
s_1 = Line(C, C_i)
t_1 = Line(B_{ce}, C_{be})
a_2 = Line(C_{ae}, A_{ce})
b_2 = Line(A_{be}, B_{ae})
A_1 = Intersect(a_2, b_2)
B_1 = Intersect(b_2, t_1)
C_1 = Intersect(t_1, a_2)
c_2 = Line(A_1, A)
d_2 = Line(B_1, B)
e_2 = Line(C, C_1)
V_i = Intersect(d_2, e_2)
X1343 = false
X1342 = false
X39 = false
Te = false
Ti = false
We = false
Wi = false
CR = false
Ve = false
Vi = false
X8160 = false
X8161 = false
Re = false
Ri = false
f_2 = EjeRadical(O_{ai}, A_e, O_{bi}, B_e)
g_2 = EjeRadical(O_{bi}, B_e, O_{ci}, C_e)
h_2 = EjeRadical(O_{ci}, C_e, O_{ai}, A_e)
R_i = Intersect(f_2, h_2)
j_2 = EjeRadical(O_{ce}, C_i, O_{be}, B_i)
k_2 = EjeRadical(O_{be}, B_i, O_{ae}, A_i)
R_e = Intersect(k_2, j_2)
i_2 = EjeRadical(O_{ce}, C_i, O_{ae}, A_i)
s_2 = Line(B_{ci}, C_{bi})
t_2 = Line(C_{ai}, A_{ci})
a_3 = Line(A_{bi}, B_{ai})
A_2 = Intersect(t_2, a_3)
B_2 = Intersect(a_3, s_2)
C_2 = Intersect(t_2, s_2)
b_3 = Line(A_2, A)
c_3 = Line(B, B_2)
d_3 = Line(C, C_2)
V_e = Intersect(d_3, c_3)
grosorApo = 1 (slider from 0 to 5, step 1)

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)