K006

P*

P*

K424a

K424b

C = (7.416775315713523, 2.009431894510515)
B = (8.717064553389815, -1.2113532687783848)
A = (2.2999724191770468, -1.1641421249306578)
m = Cubic(A, B, C, 6)
polígono1, c, a, b = Polygon(A, B, C)
P = Point(m)
polígono2, E, D, F = CuadriverticePuntosDiagonalesVertice(A, B, C, P)
polígono3, f, d, e = Polygon(D, E, F)
A_i, A_e = CentrosCuadradosInscritos(A, B, C)
g = Line(D, A_i)
h = Line(A_e, D)
B_i, B_e = CentrosCuadradosInscritos(B, C, A)
C_i, C_e = CentrosCuadradosInscritos(C, A, B)
i = Line(B_e, E)
j = Line(B_i, E)
k = Line(C_i, F)
l = Line(C_e, F)
polígono4, c_e, a_e, b_e = Polygon(A_e, B_e, C_e)
polígono5, c_i, a_i, b_i = Polygon(A_i, B_i, C_i)
Q_e = Intersect(i, l)
Q_i = Intersect(j, k)
n = Line(Q_i, Q_e)
X_2 = TriangleCenter(A, B, C, 2)
X_6 = TriangleCenter(A, B, C, 6)
X_{493} = TriangleCenter(A, B, C, 493)
X_{494} = TriangleCenter(A, B, C, 494)
X_{3069} = ConjugadoIsogonal(A, B, C, X_{494})
X_{3068} = ConjugadoIsogonal(A, B, C, X_{493})
lugar1, lugar2 = kPOmegaP(A, B, C, X_6, X_{3069})
lugar3, lugar4 = kPOmegaP(A, B, C, X_6, X_{3068})
I_a = Trilinear(A, B, C, -1, 1, 1)
p = Conic(F, D, E, Q_e, P)

Tool: CentrosCuadradosInscritos
Dar ABC
Input: A, B, C
Output: A_i, A_e

polígono1, c, a, b = Polygon(A, B, C)
B' = Rotate(B, 90*°, C)
d = Line(C, B)
e = Line(A, B')
D = Intersect(e, d)
C' = Rotate(C, 270*°, B)
f = Line(C', A)
E = Intersect(d, f)
g = OrthogonalLine(E, a)
h = Line(A, B)
F = Intersect(h, g)
A_i = Midpoint(D, F)
B'' = Mirror(B', a)
C'' = Mirror(C', a)
i = Line(B'', A)
j = Line(C'', A)
G = Intersect(d, j)
H = Intersect(i, d)
k = OrthogonalLine(G, a)
I = Intersect(h, k)
A_e = Midpoint(H, I)

Tool: Cuadrivertice PuntosDiagonales Vertice (command CuadriverticePuntosDiagonalesVertice)
Dar los puntos diagonales y un vértice
Input: A, B, C, P_1
Output: polígono2, P_2, P_3, P_4

d = Line(B, A)
e = Line(C, A)
f = Line(B, P_1)
g = Line(C, P_1)
i = Line(B, C)
D = Intersect(f, e)
E = Intersect(g, d)
h = Line(D, E)
F = Intersect(i, h)
j = Line(F, A)
P_2 = Intersect(f, j)
k = Line(P_2, C)
P_4 = Intersect(g, j)
l = Line(P_4, B)
P_3 = Intersect(l, k)
polígono2, p_1, p_2, p_3, p_4 = Polygon(P_1, P_2, P_3, P_4)

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: Triangulo Ceviano (command TrianguloCeviano)
Dar ABC y P
Input: A, B, C, P
Output: polígono2, A', B', C'

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(A, P)
h = Line(B, P)
i = Line(C, P)
A' = Intersect(d, g)
B' = Intersect(e, h)
C' = Intersect(f, i)
polígono2, f_1, d_1, e_1 = Polygon(A', B', C')

Tool: Conjugado Isotomico (command ConjugadoIsotomico1)
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: Ceviana A_PQ (command CevianaA_PQ)
Input: A, B, C, P, Q
Output: p

polígono2, D, E, F = TrianguloCeviano(A, B, C, P)
polígono3, G, H, I = TrianguloCeviano(A, B, C, Q)
e = Line(C, A)
f = Line(A, B)
g = Line(D, f)
h = Line(D, e)
i = Line(G, e)
j = Line(G, f)
J = Intersect(f, i)
K = Intersect(f, h)
L = Intersect(g, e)
M = Intersect(j, e)
k = Line(B, L)
l = Line(B, M)
m = Line(C, J)
n = Line(C, K)
N = Intersect(k, m)
O = Intersect(l, n)
p = Line(N, O)

Tool: Producto Baricentrico (command ProductoBaricentrico)
Dar ABC y dos puntos P y Q
Input: A, B, C, P, Q
Output: PQ

$P \times Q$

q = CevianaA_PQ(B, C, A, P, Q)
r = CevianaA_PQ(C, A, B, P, Q)
PQ = Intersect(q, r)

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: kP Omega P (command kPOmegaP)
Dar ABC Omega y P: da la isocúbica pivotal pK(Omega,P)
Input: A, B, C, ω, P
Output: lugar2, lugar1

$\Omega$

$P^\bullet$

P*

M/P

D = ConjugadoIsotomico(A, B, C, P)
E = ProductoBaricentrico(A, B, C, D, ω)
d = Line(P, E)
M = Point(d)
F = cocienteceviano(A, B, C, M, P)
e = Line(F, P)
f = Conic(M, E, A, B, C)
G, H = Intersect(f, e)
lugar1 = Locus(H, M)
lugar2 = Locus(G, M)

Tool: Conjugado Isogonal (command ConjugadoIsogonal)
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: G

P*

polígono1, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(P, b)
e = OrthogonalLine(P, a)
f = OrthogonalLine(P, c)
g = Line(A, B)
h = Line(B, C)
i = Line(C, A)
D = Intersect(g, f)
E = Intersect(d, i)
F = Intersect(h, e)
k = Line(E, F)
l = Line(F, D)
n = OrthogonalLine(B, l)
p = OrthogonalLine(C, k)
G = Intersect(n, p)