0

1

t

A = (-0.38074513194529325, 2.976531216341083)
C = (3.8513479081889277, 6.441557392951019)
B = (6.137245310009995, 3.0592177999288044)
polígono1, c, a, b = Polygon(A, B, C)
O = (0, 0)
U = (1, 0)
d = Line(O, U)
T = Point(d)
t: x(T)
X_2 = TriangleCenter(A, B, C, 2)
A_b = Dilate(A, t * c, B)
A_c = Dilate(A, t * b, C)
B_c = Dilate(B, t * a, C)
C_a = Dilate(C, t * b, A)
C_b = Dilate(C, t * a, B)
e = Conic(A_b, C_b, B_c, A_c, C_a)
B_a = Dilate(B, t * c, A)
W = Center(e)
D = Midpoint(a)
E = Midpoint(b)
F = Midpoint(c)
X_{6376} = Trilinear(A, B, C, b^(2) * c^(2) * (b * c - a * (b + c)), a^(2) * c^(2) * (-b * c + a * (-b + c)), a^(2) * b^(2) * (a * (b - c) - b * c))
X_{6374} = Trilinear(A, B, C, b * c * (b^(4) * c^(4) - a^(2) * b^(2) * c^(2) * (b^(2) + c^(2))), -a^(3) * b^(2) * c^(5) + a^(5) * (-b^(2) * c^(3) + c^(5)), -a^(3) * b^(5) * c^(2) + a^(5) * (b^(5) - b^(3) * c^(2)))
F_a = Trilinear(A, B, C, a * b * c, b^(2) * (b - c), c^(2) * (-b + c))
F_b = Trilinear(A, B, C, a^(2) * (a - c), a * b * c, c^(2) * (-a + c))
g = Circle(A, B, C)
F_c = Trilinear(A, B, C, a^(2) * (a - b), b^(2) * (-a + b), a * b * c)
X_4 = TriangleCenter(A, B, C, 4)
lugar3 = Locus(W, T)
texto1: "t=" + t + ""
f = Line(A_b, A_c)
i = Line(B_a, B_c)
j = Line(C_a, C_b)
A' = Intersect(i, j)
B' = Intersect(f, j)
C' = Intersect(f, i)
l = Line(C', C)
m = Line(A', A)
n = Line(B', B)
Z = Intersect(l, n)
X_{75} = TriangleCenter(A, B, C, 75)
X_{192} = TriangleCenter(A, B, C, 192)
p = Conic(A, B, C, X_{75}, X_{192})
X_{6377} = Trilinear(A, B, C, -a * (b - c)^(2) * (-b * c + a * (b + c)), -b * (a - c)^(2) * (a * (b - c) + b * c), (a - b)^(2) * c * (a * (b - c) - b * c))
polígono2 = Polygon({A', B', C'})

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: puntoRazon
Punto X que divide al segmento de extremos P y Q, según una razón  dada, PX : XQ = m : n
Input: P, Q, m, n
Output: X

X = Dilate(Q, m / (m + n), P)

Tool: Herramienta4
Input: A, C, B, k
Output: A'_1, A'

polígono1, c, a, b = Polygon(A, B, C)
A' = Dilate(A, k * c, B)
A'_1 = Dilate(A, k * b, C)