Alturas

Baricentro

Bisectrices exteriores

Bisectrices interiores

Circuncentro

Circunferencia circunscrita

Circunferencia de los 9 puntos

Circunferencia inscrita

Circunferencias de Malfatti

Circunferencias exinscritas

Exincentros

Hipérbola de Stammler

Incentro

Medianas

Mediatrices

Ortocentro

Pies de las alturas

Punto simediano

Recta de Euler

Simedianas

Triángulo de contacto interior

Triángulo de Morley

Triángulo medial

Triángulos altimediales

Triángulos de contacto exterior

Trisectrices interiores

b = %v

Punto de Fermat

A27 = 0
A1 = 0
A26 = 0
A25 = 0
A24 = 0
A23 = 0
A22 = 0
A21 = 0
A20 = 0
A19 = 0
A18 = 0
A17 = 0
A16 = 0
A15 = 0
A14 = 0
A13 = 0
A12 = 0
A11 = 0
A10 = 0
A9 = 0
A8 = 0
A7 = 0
A6 = 0
A5 = 0
A4 = 0
A3 = 0
A2 = 0
pre: A1:A27
sol: {21.0, 18.0, 12.0, 8.0, 2.0, 1.0, 25.0, 4.0, 5.0, 9.0, 11.0, 13.0, 7.0, 16.0, 3.0, 24.0, 22.0, 20.0, 26.0, 19.0, 6.0, 15.0, 17.0, 23.0, 10.0, 14.0, 27.0}
aciertos = Sequence(If[Element[pre, k] ≟ Element[sol, k], 1.0, 0.0], k, 1.0, 27.0)
a = 0 (slider from 0 to 27, step 1)
b: round(a)
A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a_1, b_1 = Polygon(A, B, C)
d, e, f = Alturas(polígono1)
D = Baricentro(polígono1)
g, h, i = BisectricesExteriores(polígono1)
j, k, l = BisectricesInteriores(polígono1)
E = Circuncentro(polígono1)
p = Circunscrita(polígono1)
q = Cir9(polígono1)
r = Inscrita(polígono1)
s, t, c_1 = Malfatti(polígono1)
d_1, e_1, f_1 = Exinscritas(polígono1)
F, G, H = Exincentros(polígono1)
g_1 = Stammler(polígono1)
I = Incentro(polígono1)
m, n, h_1 = Medianas(polígono1)
i_1, j_1, k_1 = Mediatrices(polígono1)
J = Ortocentro(polígono1)
K, L, M = AlturasPies(polígono1)
N = Simediano(polígono1)
l_1 = Euler(polígono1)
m_1, n_1, p_1 = Simedianas(polígono1)
polígono2 = ContactoInterior(polígono1)
polígono3 = Morley(polígono1)
polígono4 = Medial(polígono1)
polígono5, polígono6, polígono7 = Altimediales(polígono1)
polígono8, polígono9, polígono10 = ContactoExterior(polígono1)
q_1, r_1, s_1, t_1, a_2, b_2 = Trisectrices(polígono1)
texto1: "Lugar nº " + b
puntos = Sum(aciertos)
lista1: {Polygon[(-2.86, -12.0), (-2.86, 8.0), (-6.0, 8.0), (-6.0, -12.0)]}
B29: puntos + " puntos"
O = Fermat(polígono1)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Alturas (pies) (command AlturasPies)
Triángulo
Input: polígono1
Output: J, K, L

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)

Tool: Baricentro
Triángulo
Input: polígono1
Output: G

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
E = Midpoint(a)
F = Midpoint(b)
d = Line(B, F)
e = Line(A, E)
G = Intersect(d, e)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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 = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d, e = AngularBisector(b, a)
f, g = AngularBisector(c, a)
h, i = AngularBisector(c, b)

Tool: Circuncentro
Triángulo
Input: polígono1
Output: O

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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 = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Contacto exterior (triángulos) (command ContactoExterior)
Triángulo
Input: polígono1
Output: polígono2, polígono3, polígono4

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Incentro
Triángulo
Input: polígono1
Output: I

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Malfatti (circunferencias) (command Malfatti)
Triángulo
Input: polígono1
Output: f_2, g_2, h_2

C = (5.72, -1.04)
B = (3.72, 1.28)
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: Medial (triángulo) (command Medial)
Triángulo
Input: polígono1
Output: polígono2

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Medianas
Triángulo
Input: polígono1
Output: d, e, g

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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 = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = LineBisector(b)
e = LineBisector(a)
f = LineBisector(c)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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: Ortocentro
Triángulo
Input: polígono1
Output: H

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(B, b)
f = OrthogonalLine(A, a)
H = Intersect(f, d)

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

C = (5.72, -1.04)
B = (3.72, 1.28)
A = (-1.0662063941502087, -0.8134257520355991)
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: Simediano (punto) (command Simediano)
Triángulo
Input: polígono1
Output: Simediano

C = (5.72, -1.04)
B = (3.72, 1.28)
A = (-1.0662063941502087, -0.8134257520355991)
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: Stammler (hipérbola) (command Stammler)
Triángulo
Input: polígono1
Output: k

C = (5.72, -1.04)
B = (3.72, 1.28)
A = (-1.0662063941502087, -0.8134257520355991)
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: Ortocentro (command Ortocentro1)
Triángulo
Input: polígono1
Output: H

A = (-2.82, 1.44)
B = (0.58, 4.84)
C = (2.24, 1.54)
polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(B, b)
f = OrthogonalLine(A, a)
H = Intersect(f, d)

Tool: Euler (recta) (command Euler)
Triángulo
Input: polígono1
Output: g

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
polígono1, c, a, b = Polygon(A, B, C)
d = LineBisector(b)
e = LineBisector(a)
O = Intersect(e, d)
D = Ortocentro(polígono1)
g = Line(O, D)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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)
k = Circle(L, K, J)

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

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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: Circunscrita (circunferencia) (command Circunscrita)
Triángulo
Input: polígono1
Output: d

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
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: Fermat (punto) (command Fermat)
Triángulo
Input: polígono1
Output: Fermat

A = (-1.0662063941502087, -0.8134257520355991)
B = (3.72, 1.28)
C = (5.72, -1.04)
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)