A

B

C

$\ell_a$

$\ell_b$

$\ell_c$

KS(A'B'C')

KS(DEF)

KS(DEF)

KS(DEF)

KS(DEF)

K455

L = (-1.3395195149162646, 0.1416594283321417)
M = (19.240453608590858, 0.19464013757748122)
N = (14.445683663788346, 7.736934737784756)
polígono1, c, a, b = Polygon(L, M, N)
d = TriangleCurve(L, M, N, (A^(2) - B^(2)) * (a^(2) + a * b + b^(2) - c^(2)) * C + A * (-a^(2) + b^(2) + b * c + c^(2)) * (B^(2) - C^(2)) + B * (a^(2) - b^(2) + a * c + c^(2)) * (-A^(2) + C^(2)) = 0)
P = Point(d)
polígono2, A', B', C' = TrianguloCeviano(L, M, N, P)
X_1 = TriangleCenter(L, M, N, 1)
e = rectaEuler(M, N, X_1)
L_A = Line(A', e)
g = rectaEuler(N, L, X_1)
L_B = Line(B', g)
i = rectaEuler(L, M, X_1)
L_C = Line(C', i)
X_{21} = TriangleCenter(L, M, N, 21)
KS = Intersect(L_C, L_B)
X_{79} = TriangleCenter(L, M, N, 79)
X_{191} = TriangleCenter(L, M, N, 191)
X_2 = TriangleCenter(L, M, N, 2)
X_7 = TriangleCenter(L, M, N, 7)
X_8 = TriangleCenter(L, M, N, 8)
X_{3649} = KScevianoP(L, M, N, X_7)
X_{3650} = KScevianoP(L, M, N, X_8)
X_{3647} = KScevianoP(L, M, N, X_2)
k = ImplicitCurve({L, M, N, X_{3647}, X_{3649}, X_{3650}, X_{191}, X_{79}, X_{21}})
X_{319} = TriangleCenter(L, M, N, 319)
X_{3648} = KScevianoP(L, M, N, X_{319})

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: 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: rectaEuler
Dar los vértices de un triángulo
Input: D, E, F
Output: m

G = TriangleCenter(D, E, F, 4)
H = TriangleCenter(D, E, F, 3)
m = Line(H, G)

Tool: KS ceviano P (command KScevianoP)
Dar ABC y P sobre K455
Input: L, M, N, P
Output: KS

A

B

C

KS(DEF)

polígono1, c, a, b = Polygon(L, M, N)
d = TriangleCurve(L, M, N, (A^(2) - B^(2)) * (a^(2) + a * b + b^(2) - c^(2)) * C + A * (-a^(2) + b^(2) + b * c + c^(2)) * (B^(2) - C^(2)) + B * (a^(2) - b^(2) + a * c + c^(2)) * (-A^(2) + C^(2)) = 0)
polígono2, D, E, F = TrianguloCeviano(L, M, N, P)
X_1 = TriangleCenter(L, M, N, 1)
g = rectaEuler(N, L, X_1)
h = Line(E, g)
i = rectaEuler(L, M, X_1)
j = Line(F, i)
KS = Intersect(j, h)