C

B

A

N = (5.094377486013581, 16.25834546408096)
M = (17.700570011378723, 1.811842720112413)
L = (-0.4328485850926938, 2.002720810601587)
polígono1, c, a, b = Polygon(L, M, N)
h = TriangleCurve(L, M, N, 2 * a^(2) * A^(4) * B^(2) * c^(4) - 2 * A^(4) * b^(2) * B^(2) * c^(4) + 4 * a^(2) * A^(3) * B^(3) * c^(4) - 4 * A^(3) * b^(2) * B^(3) * c^(4) + 2 * a^(2) * A^(2) * B^(4) * c^(4) - 2 * A^(2) * b^(2) * B^(4) * c^(4) + 2 * A^(4) * B^(2) * c^(6) - 2 * A^(2) * B^(4) * c^(6) - 4 * A^(4) * b^(4) * B * c^(2) * C + a^(4) * A^(3) * B^(2) * c^(2) * C - 2 * a^(2) * A^(3) * b^(2) * B^(2) * c^(2) * C - 3 * A^(3) * b^(4) * B^(2) * c^(2) * C + 3 * a^(4) * A^(2) * B^(3) * c^(2) * C + 2 * a^(2) * A^(2) * b^(2) * B^(3) * c^(2) * C - A^(2) * b^(4) * B^(3) * c^(2) * C + 4 * a^(4) * A * B^(4) * c^(2) * C + 4 * A^(4) * b^(2) * B * c^(4) * C + 6 * a^(2) * A^(3) * B^(2) * c^(4) * C - 2 * A^(3) * b^(2) * B^(2) * c^(4) * C + 2 * a^(2) * A^(2) * B^(3) * c^(4) * C - 6 * A^(2) * b^(2) * B^(3) * c^(4) * C - 4 * a^(2) * A * B^(4) * c^(4) * C + A^(3) * B^(2) * c^(6) * C - A^(2) * B^(3) * c^(6) * C - 2 * a^(2) * A^(4) * b^(4) * C^(2) - 2 * A^(4) * b^(6) * C^(2) - a^(4) * A^(3) * b^(2) * B * C^(2) - 6 * a^(2) * A^(3) * b^(4) * B * C^(2) - A^(3) * b^(6) * B * C^(2) + a^(6) * A * B^(3) * C^(2) + 6 * a^(4) * A * b^(2) * B^(3) * C^(2) + a^(2) * A * b^(4) * B^(3) * C^(2) + 2 * a^(6) * B^(4) * C^(2) + 2 * a^(4) * b^(2) * B^(4) * C^(2) + 2 * A^(4) * b^(4) * c^(2) * C^(2) + 2 * a^(2) * A^(3) * b^(2) * B * c^(2) * C^(2) + 2 * A^(3) * b^(4) * B * c^(2) * C^(2) - 2 * a^(4) * A * B^(3) * c^(2) * C^(2) - 2 * a^(2) * A * b^(2) * B^(3) * c^(2) * C^(2) - 2 * a^(4) * B^(4) * c^(2) * C^(2) + 3 * A^(3) * b^(2) * B * c^(4) * C^(2) - 3 * a^(2) * A * B^(3) * c^(4) * C^(2) - 4 * a^(2) * A^(3) * b^(4) * C^(3) - 3 * a^(4) * A^(2) * b^(2) * B * C^(3) - 2 * a^(2) * A^(2) * b^(4) * B * C^(3) + A^(2) * b^(6) * B * C^(3) - a^(6) * A * B^(2) * C^(3) + 2 * a^(4) * A * b^(2) * B^(2) * C^(3) + 3 * a^(2) * A * b^(4) * B^(2) * C^(3) + 4 * a^(4) * b^(2) * B^(3) * C^(3) + 4 * A^(3) * b^(4) * c^(2) * C^(3) - 2 * a^(2) * A^(2) * b^(2) * B * c^(2) * C^(3) + 6 * A^(2) * b^(4) * B * c^(2) * C^(3) - 6 * a^(4) * A * B^(2) * c^(2) * C^(3) + 2 * a^(2) * A * b^(2) * B^(2) * c^(2) * C^(3) - 4 * a^(4) * B^(3) * c^(2) * C^(3) + A^(2) * b^(2) * B * c^(4) * C^(3) - a^(2) * A * B^(2) * c^(4) * C^(3) - 2 * a^(2) * A^(2) * b^(4) * C^(4) + 2 * A^(2) * b^(6) * C^(4) - 4 * a^(4) * A * b^(2) * B * C^(4) + 4 * a^(2) * A * b^(4) * B * C^(4) - 2 * a^(6) * B^(2) * C^(4) + 2 * a^(4) * b^(2) * B^(2) * C^(4) + 2 * A^(2) * b^(4) * c^(2) * C^(4) - 2 * a^(4) * B^(2) * c^(2) * C^(4) = 0)
g = Circle(L, M, N)
I_a = Trilinear(L, M, N, -1, 1, 1)
I_b = Trilinear(L, M, N, -1, 1, -1)
I_c = Trilinear(L, M, N, 1, 1, -1)
X_1 = TriangleCenter(L, M, N, 1)
X_{20} = TriangleCenter(L, M, N, 20)
X_{64} = TriangleCenter(L, M, N, 64)
X_4 = TriangleCenter(L, M, N, 4)
l = Line(X_{64}, X_4)
X_2 = TriangleCenter(L, M, N, 2)
X_{107} = TriangleCenter(L, M, N, 107)
m = Line(X_2, X_{107})
X_3 = TriangleCenter(L, M, N, 3)
L' = Mirror(L, X_3)
M' = Mirror(M, X_3)
N' = Mirror(N, X_3)
A_1 = Trilinear(L, M, N, 0, c * (a^(2) - b^(2) + c^(2)), b * (a^(2) + b^(2) - c^(2)))
B_1 = Trilinear(L, M, N, c * (-a^(2) + b^(2) + c^(2)), 0, a * (a^(2) + b^(2) - c^(2)))
C_1 = Trilinear(L, M, N, b * (-a^(2) + b^(2) + c^(2)), a * (a^(2) - b^(2) + c^(2)), 0)
d = Tangent(L, g)
e = Tangent(M, g)
f = Tangent(N, g)
X_{25} = TriangleCenter(L, M, N, 25)
i = Line(L, X_{25})
j = Line(M, X_{25})
k = Line(N, X_{25})
n = Line(L', X_{64})
p = Line(N', X_{64})
q = Line(M', X_{64})

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 Antipedal (command TrianguloAntipedal)
Dar ABC y P
Input: A, B, C, P
Output: polígono2, D, E, F

d = Segment(P, A)
e = Segment(P, B)
f = Segment(P, C)
g = OrthogonalLine(A, d)
h = OrthogonalLine(B, e)
i = OrthogonalLine(C, f)
D = Intersect(h, i)
E = Intersect(g, i)
F = Intersect(g, h)
polígono2, f_1, d_1, e_1 = Polygon(D, E, F)

Tool: Triangulo Pedal (command TrianguloPedal)
Dar ABC y P
Input: A, B, C, E
Output: polígono2, F, G, H

polígono1, c, a, b = Polygon(A, B, C)
e = OrthogonalLine(E, a)
f = OrthogonalLine(E, b)
g = OrthogonalLine(E, c)
h = Line(B, C)
i = Line(C, A)
j = Line(A, B)
F = Intersect(e, h)
G = Intersect(i, f)
H = Intersect(j, g)
polígono2, h_1, f_1, g_1 = Polygon(F, G, H)