C

B

A

$\mathbf{C^+}$

N = (12.15728252043596, 15.56704395014581)
M = (19.14042520982027, 4.275500396627892)
L = (-1.474408563010394, 5.134451803829175)
polígono1, c, a, b = Polygon(L, M, N)
o = TriangleCurve(L, M, N, a^(4) * A^(2) * B - A^(2) * b^(4) * B + a^(4) * A * B^(2) - A * b^(4) * B^(2) - 2 * a^(2) * A^(2) * B * c^(2) + 2 * A * b^(2) * B^(2) * c^(2) + A^(2) * B * c^(4) - A * B^(2) * c^(4) + a^(2) * A^(2) * B * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) - A^(2) * b^(2) * B * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) + a^(2) * A * B^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) - A * b^(2) * B^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) - A^(2) * B * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) + A * B^(2) * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) - a^(4) * A^(2) * C + 2 * a^(2) * A^(2) * b^(2) * C - A^(2) * b^(4) * C + a^(4) * B^(2) * C - 2 * a^(2) * b^(2) * B^(2) * C + b^(4) * B^(2) * C + A^(2) * c^(4) * C - B^(2) * c^(4) * C - a^(2) * A^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C + A^(2) * b^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C - a^(2) * B^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C + b^(2) * B^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C + A^(2) * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C - B^(2) * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C - a^(4) * A * C^(2) + A * b^(4) * C^(2) - a^(4) * B * C^(2) + b^(4) * B * C^(2) - 2 * A * b^(2) * c^(2) * C^(2) + 2 * a^(2) * B * c^(2) * C^(2) + A * c^(4) * C^(2) - B * c^(4) * C^(2) - a^(2) * A * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) - A * b^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) + a^(2) * B * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) + b^(2) * B * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) + A * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) - B * c^(2) * sqrt(-a^(4) + 2 * a^(2) * b^(2) - b^(4) + 2 * a^(2) * c^(2) + 2 * b^(2) * c^(2) - c^(4)) * C^(2) = 0)
P = Point(o)
polígono2, D, E, F = TrianguloCeviano(L, M, N, P)
B'_1 = Rotate(M, 45*°, N)
C'_1 = Rotate(N, 315*°, M)
d = Line(M, C'_1)
e = Line(N, B'_1)
f = Line(D, e)
g = Line(D, d)
D_a = Intersect(d, e)
D_c = Intersect(e, g)
D_b = Intersect(d, f)
h = Circle(D_a, D)
k = Circle(D_c, M)
p = Circle(D_b, N)
i = EjeRadical(D_a, D, D_c, M)
j = EjeRadical(D_c, M, D_b, N)
A' = Intersect(j, i)
B' = Herramienta5(M, N, L, P)
C' = Herramienta5(N, L, M, P)
l = Line(L, A')
m = Line(M, B')
n = Line(N, C')
q = Semicircle(D, M)
r = Semicircle(N, D)
s = Semicircle(N, M)
Q = Intersect(m, n)
X_4 = TriangleCenter(L, M, N, 4)
X_2 = TriangleCenter(L, M, N, 2)
X_{492} = TriangleCenter(L, M, N, 492)
X_{193} = TriangleCenter(L, M, N, 193)
X_{1585} = TriangleCenter(L, M, N, 1585)
t = Semicircle(L, N)
d_1 = Semicircle(E, N)
f_1 = Semicircle(L, E)
a_1 = LineBisector(L, B')
b_1 = LineBisector(E, N)
E_c = Intersect(a_1, b_1)
c_1 = LineBisector(L, N)
e_1 = LineBisector(E, B')
E_b = Intersect(e_1, c_1)
g_1 = LineBisector(E, L)
h_1 = LineBisector(B', N)
E_a = Intersect(g_1, h_1)
k_1 = Semicircle(M, L)
p_1 = Semicircle(M, F)
q_1 = Semicircle(F, L)
i_1 = LineBisector(L, M)
j_1 = LineBisector(C', F)
F_c = Intersect(j_1, i_1)
l_1 = LineBisector(L, F)
m_1 = LineBisector(M, C')
F_a = Intersect(m_1, l_1)
n_1 = LineBisector(F, M)
r_1 = LineBisector(L, C')
F_b = Intersect(r_1, n_1)

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: EjeRadical
Dar centro, punto y centro, punto
Input: A, B, C, D
Output: i

e = Circle(B, D, A)
E = Center(e)
a = Segment(A, E)
b = Segment(E, C)
B' = Mirror(B, a)
D' = Mirror(D, b)
f = Segment(A, C)
g = Line(B, B')
h = Line(D', D)
F = Intersect(g, h)
i = OrthogonalLine(F, f)

Tool: Herramienta5
Input: A, B, C, P
Output: A'

polígono2, D, E, F = TrianguloCeviano(A, B, C, P)
B' = Rotate(B, 45*°, C)
C' = Rotate(C, 315*°, B)
d = Line(B, C')
e = Line(C, B')
f = Line(D, e)
g = Line(D, d)
G = Intersect(d, e)
H = Intersect(e, g)
I = Intersect(d, f)
i = EjeRadical(G, D, H, B)
j = EjeRadical(H, B, I, C)
A' = Intersect(j, i)