Círculos de Stammler

Hipérbola de Stammler

Triángulo de Morley

Medianas

Bisectrices interiores

Punto simediano

Circunferencia 9 puntos

Punto de Fermat

Primer punto isogónico

Segundo punto isogónico

Trisectrices interiores

Simedianas

Incentro

Exincentros

Circuncentro

Bisectrices exteriores

B = (9.219999999999999, -0.5999999999999999)
A = (2.3, -0.37999999999999995)
C = (6.999999999999999, 1.4599999999999997)
trianguloABC, c, a, b = Polygon(A, B, C)
d = Line(A, C)
e = Line(C, B)
f = Line(A, B)
r = 2.1 (slider from 0.5 to 5, step 0.1)
g, h, k, D = rHipérbolas(trianguloABC, r)
p = Circle(D, r)
q = Stammler(trianguloABC)
verCS = false
verHS = false
verTM = false
verM = false
verBI = false
verK = false
verC9 = false
verF = false
verI1 = false
verI2 = false
verTI = false
verS = false
verI = false
verE = false
verO = false
texto1: "r = " + r
O = Circuncentro(trianguloABC)
verBE = false
c_1, d_1, e_1 = BisectricesInteriores(trianguloABC)
I = Incentro(trianguloABC)
f_1, g_1, h_1 = BisectricesExteriores(trianguloABC)
J_A, J_B, J_C = Exincentros(trianguloABC)
i_1, j_1, k_1, l_1, m_1, n_1 = Trisectrices(trianguloABC)
polígono1 = Morley(trianguloABC)
E = X14(trianguloABC)
i = LineBisector(b)
j = LineBisector(a)
l = OrthogonalLine(B, i)
m = OrthogonalLine(A, j)
H = Intersect(j, m)
J = Intersect(i, l)
t = Circle(C, B)
p_1 = Circle(A, C)
n = LineBisector(b)
s = LineBisector(a)
F = Midpoint(b)
G = Midpoint(a)
a_1 = OrthogonalLine(B, n)
b_1 = OrthogonalLine(A, s)
K_1 = Intersect(s, b_1)
L = Intersect(n, a_1)
L' = Mirror(L, F)
K' = Mirror(K_1, G)
q_1 = Ray(G, K')
r_1 = Ray(F, L')
s_1 = Circle(C, B)
t_1 = Circle(C, A)
M = Intersect(t_1, r_1, 1.0)
N = Intersect(s_1, q_1, 1.0)
a_2 = Line(A, N)
b_2 = Line(M, B)
P = Intersect(a_2, b_2)
panel: {Polygon[(-0.44, -15.0), (-0.44, 15.0), (-6.0, 15.0), (-6.0, -15.0)]}
Q = Fermat(trianguloABC)
c_2, d_2, e_2 = Medianas(trianguloABC)
f_2, g_2, h_2 = Simedianas(trianguloABC)
K = Simediano(trianguloABC)
k_2 = Cir9(trianguloABC)
α = Angle(A, P, B)
β = Angle(A, P, C)
γ = Angle(B, P, C)
δ = Angle(A, E, B)
ε = Angle(A, E, C)
ζ = Angle(B, E, C)
i_2 = Segment(E, B)
j_2 = Segment(E, C)
l_2 = Segment(E, A)
m_2 = Segment(P, A)
n_2 = Segment(P, B)
p_2 = Segment(P, C)

Tool: Circuncentro
Triángulo
Input: polígono1
Output: O

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d = LineBisector(b)
e = LineBisector(a)
O = Intersect(e, d)

Tool: Exincentros
Triángulo
Input: polígono1
Output: E_A, E_B, E_C

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d_2, e_2 = AngularBisector(b, a)
d_1, e_1 = AngularBisector(b, a)
h_1, i_1 = AngularBisector(c, b)
h, i = AngularBisector(c, b)
E_C = Intersect(e_1, h)
E_A = Intersect(d_1, i)
E_B = Intersect(d_1, h)

Tool: Fermat (punto) (command Fermat)
Triángulo
Input: polígono1
Output: Fermat

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
A' = Intersect(c, b)
B' = Intersect(a, c)
C' = Intersect(a, b)
q = Circle(C', A')
g = LineBisector(b)
f = LineBisector(a)
E = Midpoint(b)
e = Line(B', E)
D = Midpoint(a)
d = Line(A', D)
F = Intersect(d, e)
F' = Mirror(F, E)
i = OrthogonalLine(F', g)
G = Intersect(g, i)
k = Ray(E, G)
K = Intersect(q, k, 1.0)
l = Line(K, B')
F'_1 = Mirror(F, D)
h = OrthogonalLine(F'_1, f)
H = Intersect(f, h)
p = Circle(C', B')
j = Ray(D, H)
J = Intersect(p, j, 1.0)
m = Line(J, A')
α = Angle(B', A', C')
β = Angle(C', B', A')
γ = Angle(A', C', B')
δ = Max({α, β, γ})
Vertice = If(δ ≟ α, A', If[δ ≟ β, B', C'])
I = Intersect(l, m)
Fermat = If(δ < 2.0 * 3.141592653589793 / 3.0, I, Vertice)

Tool: Incentro
Triángulo
Input: polígono1
Output: I

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
h, i = AngularBisector(c, b)
I = Intersect(e_1, i)

Tool: Simediano (punto) (command Simediano)
Triángulo
Input: polígono1
Output: Simediano

C = (6.999999999999999, 1.4599999999999997)
B = (9.219999999999999, -0.5999999999999999)
A = (2.3, -0.37999999999999995)
polígono1, c, a, b = Polygon(A, B, C)
H = Point(a)
F = Midpoint(b)
E = Midpoint(a)
k = Line(H, E)
D = Midpoint(c)
G = Point(b)
l = Line(G, F)
C' = Intersect(l, k)
I = Point(c)
j = Line(I, D)
A' = Intersect(l, j)
B' = Intersect(k, j)
f = AngularBisector(C', A', B')
i = AngularBisector(B', C', A')
e = Line(A', E)
e' = Mirror(e, f)
g = Line(C', D)
g' = Mirror(g, i)
Simediano = Intersect(e', g')

Tool: Bisectrices exteriores (command BisectricesExteriores)
Triángulo
Input: polígono1
Output: d_1, f_1, h

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
f_1, g = AngularBisector(c, a)
h, i = AngularBisector(c, b)

Tool: Bisectrices interiores (command BisectricesInteriores)
Triángulo
Input: polígono1
Output: e, g, i

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d, e = AngularBisector(b, a)
f, g = AngularBisector(c, a)
h, i = AngularBisector(c, b)

Tool: Medianas
Triángulo
Input: polígono1
Output: d, e, g

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
D = Midpoint(c)
E = Midpoint(a)
F = Midpoint(b)
d = Line(B, F)
e = Line(A, E)
g = Line(C, D)

Tool: Mediatrices
Triángulo
Input: polígono1
Output: d, e, f

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = LineBisector(b)
e = LineBisector(a)
f = LineBisector(c)

Tool: Simedianas
Triángulo
Input: polígono1
Output: d', e', g'

C = (6.999999999999999, 1.4599999999999997)
B = (9.219999999999999, -0.5999999999999999)
A = (2.3, -0.37999999999999995)
polígono1, c, a, b = Polygon(A, B, C)
H = Point(a)
F = Midpoint(b)
E = Midpoint(a)
k = Line(H, E)
D = Midpoint(c)
G = Point(b)
l = Line(G, F)
C' = Intersect(l, k)
I = Point(c)
j = Line(I, D)
A' = Intersect(l, j)
B' = Intersect(k, j)
f = AngularBisector(C', A', B')
h = AngularBisector(A', B', C')
i = AngularBisector(B', C', A')
e = Line(A', E)
e' = Mirror(e, f)
d = Line(B', F)
d' = Mirror(d, h)
g = Line(C', D)
g' = Mirror(g, i)

Tool: Trisectrices interiores (command Trisectrices)
Triángulo
Input: polígono1
Output: a_1, b_1, i, r, s, l

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
D = Point(c)
E = Point(c)
F = Point(a)
G = Point(a)
H = Point(b)
I = Point(b)
d = Line(D, E)
e = Line(F, G)
f = Line(I, H)
A' = Intersect(f, d)
B' = Intersect(e, d)
C' = Intersect(f, e)
α = Angle(C', A', B')
β = Angle(A', B', C')
γ = Angle(B', C', A')
C'' = Rotate(C', α / 3.0, A')
g = Ray(A', C'')
J = Intersect(a, g)
C''' = Mirror(C'', b)
h = Ray(A', C''')
J' = Intersect(a, h)
JJ = If(Defined[J], J, J')
i = Segment(A', JJ)
A'' = Rotate(A', β / 3.0, B')
j = Ray(B, A'')
K = Intersect(b, j)
A''' = Mirror(A'', c)
k = Ray(B, A''')
K' = Intersect(b, k)
KK = If(Defined[K], K, K')
l = Segment(B', KK)
m = AngularBisector(JJ, A', B')
B'' = Rotate(B', γ / 3.0, C')
p = Ray(C, B'')
N = Intersect(c, p)
B''' = Mirror(B'', a)
q = Ray(C, B''')
N' = Intersect(c, q)
NN = If(Defined[N], N, N')
r = Segment(C', NN)
n = AngularBisector(KK, B', C')
t = AngularBisector(NN, C', A')
Q = Intersect(m, a)
R = Intersect(t, c)
S = Intersect(n, b)
s = Segment(A, Q)
a_1 = Segment(C, R)
b_1 = Segment(B, S)

Tool: 9 puntos (circunferencia) (command Cir9)
Triángulo
Input: polígono1
Output: k

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(B, b)
e = OrthogonalLine(C, c)
f = OrthogonalLine(A, a)
G = Midpoint(b)
H = Midpoint(a)
I = Midpoint(c)
D = Point(b)
E = Point(c)
F = Point(a)
g = Line(E, I)
h = Line(D, G)
i = Line(H, F)
J = Intersect(h, d)
K = Intersect(f, i)
L = Intersect(g, e)
k = Circle(L, K, J)

Tool: Circunscrita (circunferencia) (command Circunscrita)
Triángulo
Input: polígono1
Output: d

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = Circle(Intersect[a, b], Intersect[a, c], Intersect[c, b])

Tool: Exinscritas (circunferencias) (command Exinscritas)
Triángulo
Input: polígono1
Output: k, p, q

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d_2, e_2 = AngularBisector(b, a)
d_1, e_1 = AngularBisector(b, a)
h_1, i_1 = AngularBisector(c, b)
h, i = AngularBisector(c, b)
E_C = Intersect(e_1, h)
E_A = Intersect(d_1, i)
E_B = Intersect(d_1, h)
d = OrthogonalLine(E_A, a)
e = OrthogonalLine(E_C, c)
D = Intersect(e, c)
E = Intersect(d, a)
f = OrthogonalLine(E_B, b)
F = Intersect(f, b)
k = Circle(E_A, E)
p = Circle(E_C, D)
q = Circle(E_B, F)

Tool: Inscrita (circunferencia) (command Inscrita)
Triángulo
Input: polígono1
Output: e

A = (1.68, -0.74)
B = (8.5, -1)
C = (5.318737464972353, 5.034044480345349)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
h, i = AngularBisector(c, b)
I = Intersect(e_1, i)
d = OrthogonalLine(I, a)
D = Intersect(d, a)
e = Circle(I, D)

Tool: Malfatti (circunferencias) (command Malfatti)
Triángulo
Input: polígono1
Output: f_2, g_2, h_2

C = (5.72, -1.04)
B = (3.74, 1.06)
A = (-1.0662063941502087, -0.8134257520355991)
polígono1, c, a, b = Polygon(A, B, C)
U = Point(c)
h, i = AngularBisector(c, b)
d_1, e_1 = AngularBisector(b, a)
I = Intersect(e_1, i)
j = AngularBisector(U, A, I)
d = AngularBisector(U, B, I)
D = Intersect(d, j)
t = OrthogonalLine(D, c)
G = Intersect(t, c)
l = AngularBisector(C, B, I)
m = AngularBisector(B, C, I)
E = Intersect(l, m)
q = AngularBisector(A, C, I)
r = AngularBisector(C, A, I)
F = Intersect(q, r)
b_1 = OrthogonalLine(F, b)
J = Intersect(b_1, b)
i_1 = Line(D, F)
K = Intersect(i_1, i)
j_1 = OrthogonalLine(K, i_1)
i' = Mirror(i, j_1)
m_1 = Line(E, F)
M = Intersect(m_1, e_1)
n_1 = OrthogonalLine(M, m_1)
p_1 = Mirror(e_1, n_1)
N = Intersect(i', p_1)
s = AngularBisector(N, G, A)
n = AngularBisector(N, J, A)
a_1 = OrthogonalLine(E, a)
H = Intersect(a_1, a)
p = AngularBisector(N, G, B)
f = AngularBisector(N, H, B)
k = AngularBisector(N, J, C)
e = AngularBisector(N, H, C)
P = Intersect(f, p)
c_2 = OrthogonalLine(P, c)
Q = Intersect(n, s)
d_2 = OrthogonalLine(Q, b)
O = Intersect(k, e)
e_2 = OrthogonalLine(O, a)
R = Intersect(c_2, c)
S = Intersect(e_2, a)
T = Intersect(d_2, b)
f_2 = Circle(O, S)
g_2 = Circle(P, R)
h_2 = Circle(Q, T)

Tool: Antimedial (triángulo) (command Antimedial)
Triángulo
Input: polígono1
Output: polígono4

A = (12.760000000000014, 9.02)
B = (0.7600000000000149, -6.6600000000000055)
C = (24.200000000000024, -2.9000000000000044)
polígono1, c, a, b = Polygon(A, B, C)
C' = Intersect(a, b)
A' = Intersect(c, b)
B' = Intersect(c, a)
e = Line(B', b)
f = Line(A', a)
g = Line(C', c)
D = Intersect(e, f)
E = Intersect(e, g)
F = Intersect(f, g)
polígono4, e_2, d, f_2 = Polygon(D, F, E)

Tool: Contacto exterior (triángulos) (command ContactoExterior)
Triángulo
Input: polígono1
Output: polígono2, polígono3, polígono4

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d_3, e_3 = AngularBisector(b, a)
d_1, e_1 = AngularBisector(b, a)
h_1, i_1 = AngularBisector(c, b)
h, i = AngularBisector(c, b)
E_C = Intersect(e_1, h)
E_A = Intersect(d_1, i)
E_B = Intersect(d_1, h)
d = OrthogonalLine(E_A, a)
e = OrthogonalLine(E_C, c)
D = Intersect(e, c)
E = Intersect(d, a)
f = OrthogonalLine(E_B, b)
F = Intersect(f, b)
k = Circle(E_A, E)
p = Circle(E_C, D)
q = Circle(E_B, F)
G = Point(c)
H = Point(c)
I = Point(a)
J = Point(a)
K = Point(b)
L = Point(b)
j = Line(I, J)
l = Line(L, K)
m = Line(H, G)
M = Intersect(p, j, 1.0)
N = Intersect(p, l, 1.0)
O = Intersect(q, m, 1.0)
P = Intersect(q, j, 1.0)
Q = Intersect(k, l, 1.0)
R = Intersect(k, m, 1.0)
polígono2, r, e_2, q_1 = Polygon(E, Q, R)
polígono3, m_1, n, d_2 = Polygon(N, D, M)
polígono4, p_1, o, f_2 = Polygon(O, F, P)

Tool: Contacto interior (triángulo) (command ContactoInterior)
Triángulo
Input: polígono1
Output: polígono2

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
h, i = AngularBisector(c, b)
I = Intersect(e_1, i)
d = OrthogonalLine(I, a)
D = Intersect(d, a)
e = Circle(I, D)
E = Intersect(e, c, 1.0)
F = Intersect(e, b, 1.0)
polígono2, f, e_2, d_2 = Polygon(E, D, F)

Tool: Medial (triángulo) (command Medial)
Triángulo
Input: polígono1
Output: polígono2

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
G = Midpoint(b)
H = Midpoint(a)
I = Midpoint(c)
polígono2, i, g, h = Polygon(G, H, I)

Tool: Morley (triángulo) (command Morley)
Triángulo
Input: polígono1
Output: polígono2

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
D = Point(c)
E = Point(c)
F = Point(a)
G = Point(a)
H = Point(b)
I = Point(b)
d = Line(D, E)
e = Line(F, G)
f = Line(I, H)
A' = Intersect(f, d)
B' = Intersect(e, d)
C' = Intersect(f, e)
α = Angle(C', A', B')
β = Angle(A', B', C')
γ = Angle(B', C', A')
C'' = Rotate(C', α / 3.0, A')
g = Ray(A', C'')
J = Intersect(a, g)
C''' = Mirror(C'', b)
h = Ray(A', C''')
J' = Intersect(a, h)
JJ = If(Defined[J], J, J')
i = Segment(A', JJ)
A'' = Rotate(A', β / 3.0, B')
j = Ray(B, A'')
K = Intersect(b, j)
A''' = Mirror(A'', c)
k = Ray(B, A''')
K' = Intersect(b, k)
KK = If(Defined[K], K, K')
l = Segment(B', KK)
m = AngularBisector(JJ, A', B')
L = Intersect(m, l)
B'' = Rotate(B', γ / 3.0, C')
p = Ray(C, B'')
N = Intersect(c, p)
B''' = Mirror(B'', a)
q = Ray(C, B''')
N' = Intersect(c, q)
NN = If(Defined[N], N, N')
r = Segment(C', NN)
n = AngularBisector(KK, B', C')
O = Intersect(n, r)
t = AngularBisector(NN, C', A')
P = Intersect(t, i)
polígono2, p_1, l_1, o = Polygon(L, O, P)

Tool: Conjugado isogonal (command Isogonal)
Triángulo, Punto
Input: polígono1, P
Output: P'

A = (1.68, -0.74)
B = (8.5, -1)
C = (6.48, 1.1399999999999988)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
h, i = AngularBisector(c, b)
d = Line(A, P)
f = Line(C, P)
d' = Mirror(d, i)
f' = Mirror(f, e_1)
P' = Intersect(d', f')

Tool: Stammler (hipérbola) (command Stammler)
Triángulo
Input: polígono1
Output: k

C = (6.999999999999999, 1.4599999999999997)
B = (9.219999999999999, -0.5999999999999999)
A = (2.3, -0.37999999999999995)
polígono1, c, a, b = Polygon(A, B, C)
J = Point(a)
H = Point(a)
l = Line(J, H)
G = Point(b)
F = Point(b)
m = Line(G, F)
C' = Intersect(m, l)
E = Point(c)
D = Point(c)
n = Line(D, E)
A' = Intersect(n, m)
B' = Intersect(l, n)
d_2, e_2 = AngularBisector(b, a)
d_1, e_1 = AngularBisector(b, a)
h_1, i_1 = AngularBisector(c, b)
h, i = AngularBisector(c, b)
E_C = Intersect(e_1, h)
E_A = Intersect(d_1, i)
E_B = Intersect(d_1, h)
d = LineBisector(a)
e = LineBisector(b)
f = AngularBisector(B', C', A')
j = AngularBisector(A', B', C')
I = Intersect(f, j)
O = Intersect(d, e)
k = Conic(E_A, E_B, E_C, O, I)

Tool: r-Hipérbolas (command rHipérbolas)
Triángulo, radio
Input: polígono1, r
Output: rHA, rHB, q_1, P

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
D = Point(c)
E = Point(c)
F = Point(a)
G = Point(a)
H = Point(b)
I = Point(b)
d = Line(D, E)
e = Line(F, G)
f = Line(H, I)
A' = Intersect(d, f)
B' = Intersect(d, e)
C' = Intersect(e, f)
J = Midpoint(c)
K_1 = Midpoint(a)
g = Line(C', J)
h = Line(A', K_1)
i = AngularBisector(A', C', B')
j = AngularBisector(B', A', C')
h' = Mirror(h, j)
g' = Mirror(g, i)
K = Intersect(h', g')
k = LineBisector(c)
l = LineBisector(a)
O = Intersect(k, l)
p = Circle(A', r)
m = Line(A', O)
n = Line(A', K)
q = OrthogonalLine(A', n)
L, M = Intersect(p, q)
N, P_1 = Intersect(p, m)
Q = Intersect(p, n, 2.0)
A''_1 = Mirror(A', Q)
s = Line(A''_1, m)
t = Circle(Q, M)
R = Intersect(t, s, 2.0)
c_1 = Conic(N, P_1, M, L, R)
a_1 = Line(B', O)
b_1 = Line(B', K)
d_1 = Circle(B', r)
e_1 = OrthogonalLine(B', b_1)
S, T = Intersect(d_1, e_1)
U, V = Intersect(d_1, a_1)
W = Intersect(d_1, b_1, 2.0)
f_1 = Circle(W, S)
B'' = Mirror(B', W)
g_1 = Line(B'', a_1)
Z = Intersect(f_1, g_1, 2.0)
h_1 = Conic(V, U, S, T, Z)
i_1 = Line(C', K)
j_1 = Line(C', O)
k_1 = Circle(C', r)
l_1 = OrthogonalLine(C', i_1)
A_1, B_1 = Intersect(k_1, l_1)
C_1, D_1 = Intersect(k_1, j_1)
E_1 = Intersect(k_1, i_1, 2.0)
C'' = Mirror(C', E_1)
m_1 = Line(C'', j_1)
p_1 = Circle(E_1, B_1)
F_1 = Intersect(p_1, m_1, 1.0)
q_1 = Conic(C_1, D_1, A_1, B_1, F_1)
P1, P3, P4, P2 = Intersect(c_1, h_1)
lista = RemoveUndefined({Distance[P1, O], Distance[P2, O], Distance[P3, O], Distance[P4, O]})
min = Min(lista)
P = If(Element[lista, 1.0] ≟ min, P1, If[Element[lista, 2.0] ≟ min, P2, If[Element[lista, 3.0] ≟ min, P3, P4]])
rHA: c_1
rHB: h_1

Tool: Altimediales (triángulos) (command Altimediales)
Triángulo
Input: polígono1
Output: polígono2, polígono3, polígono4

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.74, 1.06)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(B, b)
e = OrthogonalLine(C, c)
f = OrthogonalLine(A, a)
G = Midpoint(b)
H = Midpoint(a)
I = Midpoint(c)
D = Point(b)
E = Point(c)
F = Point(a)
g = Line(E, I)
h = Line(D, G)
i = Line(H, F)
J = Intersect(h, d)
K = Intersect(f, i)
L = Intersect(g, e)
polígono2, i_1, j, h_1 = Polygon(J, H, I)
polígono3, h_2, l, g_1 = Polygon(L, G, H)
polígono4, g_2, k, i_2 = Polygon(K, I, G)

Tool: X14
Triángulo
Input: polígono1
Output: X14

A = (2.3, -0.37999999999999995)
B = (9.219999999999999, -0.5999999999999999)
C = (6.999999999999999, 1.4599999999999997)
polígono1, c, a, b = Polygon(A, B, C)
A' = Intersect(c, b)
B' = Intersect(a, c)
C' = Intersect(a, b)
q = Circle(C', A')
g = LineBisector(b)
f = LineBisector(a)
E = Midpoint(b)
e = Line(B', E)
D = Midpoint(a)
d = Line(A', D)
F = Intersect(d, e)
i = OrthogonalLine(F, g)
G = Intersect(g, i)
k = Ray(E, G)
K = Intersect(q, k, 1.0)
l = Line(K, B')
h = OrthogonalLine(F, f)
H = Intersect(f, h)
p = Circle(C', B')
j = Ray(D, H)
J = Intersect(p, j, 1.0)
m = Line(J, A')
X14 = Intersect(l, m)