A

B

C

Euler line

$M^a$

$M^b$

$M^c$

Q006

L = (14.413491831701498, -1.8160069977782045)
M = (26.482599795389778, -1.9237668903111362)
N = (21.283184980675856, 7.639923571986559)
polígono1, c, a, b = Polygon(L, M, N)
Q066 = TriangleCurve(L, M, N, a^(2) * A^(2) * B^(2) * c^(2) - A^(2) * b^(2) * B^(2) * c^(2) - a^(2) * A^(2) * b^(2) * C^(2) + a^(2) * b^(2) * B^(2) * C^(2) + A^(2) * b^(2) * c^(2) * C^(2) - a^(2) * B^(2) * c^(2) * C^(2) = 0)
k = Circle(L, M, N)
d = Line(L, M)
e = Line(L, N)
b_1 = Line(M, N)
P = Point(Q066)
polígono2, D, E, F = TrianguloCeviano(L, M, N, P)
f = Line(L, P)
E_b = Midpoint(M, E)
F_c = Midpoint(N, F)
g = Line(E_b, F_c)
D_a = Midpoint(E, F)
h = Circle(E_b, F_c, D_a)
J = Center(h)
polígono3, f_1, d_1, e_1 = Polygon(D, E, F)
i = OrthogonalLine(J, d_1)
D' = Mirror(D_a, i)
A' = Mirror(D', g)
K = Midpoint(M, N)
L_1 = Midpoint(N, L)
M_1 = Midpoint(L, M)
p = Circle(K, L_1, M_1)
j = Line(A', K)
l = Line(L, A')
B', m, n = AA'(M, N, L, P)
C', q, r = AA'(N, L, M, P)
polígono4, o, i'', n_1 = Polygon(A', B', C')
Q = Intersect(q, m)
lgQ066 = TriangleCurve(L, M, N, A^(2) * B^(2) * (-a^(10) + 3 * a^(8) * b^(2) - 2 * a^(6) * b^(4) - 2 * a^(4) * b^(6) + 3 * a^(2) * b^(8) - b^(10) + a^(8) * c^(2) - 4 * a^(6) * b^(2) * c^(2) + 6 * a^(4) * b^(4) * c^(2) - 4 * a^(2) * b^(6) * c^(2) + b^(8) * c^(2)) + A^(2) * B * (2 * a^(10) - 4 * a^(8) * b^(2) + 2 * a^(6) * b^(4) - 4 * a^(8) * c^(2) + 8 * a^(6) * b^(2) * c^(2) - 4 * a^(4) * b^(4) * c^(2) + 2 * a^(6) * c^(4) - 4 * a^(4) * b^(2) * c^(4) + 2 * a^(2) * b^(4) * c^(4)) * C + A * B^(2) * (2 * a^(4) * b^(6) - 4 * a^(2) * b^(8) + 2 * b^(10) - 4 * a^(4) * b^(4) * c^(2) + 8 * a^(2) * b^(6) * c^(2) - 4 * b^(8) * c^(2) + 2 * a^(4) * b^(2) * c^(4) - 4 * a^(2) * b^(4) * c^(4) + 2 * b^(6) * c^(4)) * C + A^(2) * (-a^(10) + a^(8) * b^(2) + 3 * a^(8) * c^(2) - 4 * a^(6) * b^(2) * c^(2) - 2 * a^(6) * c^(4) + 6 * a^(4) * b^(2) * c^(4) - 2 * a^(4) * c^(6) - 4 * a^(2) * b^(2) * c^(6) + 3 * a^(2) * c^(8) + b^(2) * c^(8) - c^(10)) * C^(2) + B^(2) * (a^(2) * b^(8) - b^(10) - 4 * a^(2) * b^(6) * c^(2) + 3 * b^(8) * c^(2) + 6 * a^(2) * b^(4) * c^(4) - 2 * b^(6) * c^(4) - 4 * a^(2) * b^(2) * c^(6) - 2 * b^(4) * c^(6) + a^(2) * c^(8) + 3 * b^(2) * c^(8) - c^(10)) * C^(2) + A * B * (2 * a^(4) * b^(4) * c^(2) - 4 * a^(4) * b^(2) * c^(4) - 4 * a^(2) * b^(4) * c^(4) + 2 * a^(4) * c^(6) + 8 * a^(2) * b^(2) * c^(6) + 2 * b^(4) * c^(6) - 4 * a^(2) * c^(8) - 4 * b^(2) * c^(8) + 2 * c^(10)) * C^(2) = 0)
X_1 = TriangleCenter(L, M, N, 1)
X_2 = TriangleCenter(L, M, N, 2)
X_4 = TriangleCenter(L, M, N, 4)
t = Line(X_4, X_2)
X_{1113} = TriangleCenter(L, M, N, 1113)
X_{1114} = TriangleCenter(L, M, N, 1114)
X_{1313} = TriangleCenter(L, M, N, 1313)
X_{1312} = TriangleCenter(L, M, N, 1312)
X_{12} = TriangleCenter(L, M, N, 12)
X_{68} = TriangleCenter(L, M, N, 68)
X_{254} = TriangleCenter(L, M, N, 254)
X_{252} = TriangleCenter(L, M, N, 252)
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)
L' = Mirror(L, K)
M' = Mirror(M, L_1)
N' = Mirror(N, M_1)
a_1 = Segment(E_b, F_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: 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: AA'
Dar ABC y P
Input: A, B, C, P
Output: I'', l, j

polígono2, D, E, F = TrianguloCeviano(A, B, C, P)
G = Midpoint(B, E)
H = Midpoint(C, F)
g = Line(G, H)
I = Midpoint(E, F)
h = Circle(G, H, I)
J = Center(h)
polígono3, f_1, d_1, e_1 = Polygon(D, E, F)
i = OrthogonalLine(J, d_1)
I' = Mirror(I, i)
I'' = Mirror(I', g)
K = Midpoint(B, C)
j = Line(I'', K)
l = Line(A, I'')