θ

tripolar de X_4

A = (1.876438566730116, 7.160863179947987)
B = (12.738588968745894, 7.141089730173103)
C = (9.240559520578417, 10.844885616468082)
polígono1, c, a, b = Polygon(A, B, C)
O = (0, 0)
U = (1, 0)
d = Line(O, U)
M = Point(d)
θ: x(M)
C' = Rotate(C, θ, A)
B' = Rotate(B, -θ, A)
e = Line(A, B')
f = Line(A, C')
g = OrthogonalLine(C, b)
h = OrthogonalLine(B, c)
B_a = Intersect(e, h)
C_a = Intersect(f, g)
i = Line(B_a, C_a)
polígono2, b_a, a_1, b_1 = Polygon(A, B, B_a)
polígono3, c_a, a_2, c_1 = Polygon(A, C, C_a)
k = Circle(A, B, C)
X_6 = TriangleCenter(A, B, C, 6)
polígono4, D, E, F = TrianguloCircunceviano(A, B, C, X_6)
G = Midpoint(a)
j = Line(A, G)
p = Parabola(D, j)
l = Polar(B, p)
m = Polar(C, p)
T_a = Intersect(m, l)
q, T_b = ParabolaHG21113(B, C, A)
r, T_c = ParabolaHG21113(C, A, B)
n = Line(T_b, T_c)
H = Midpoint(A, C)
I = Midpoint(A, B)
s = Line(B, H)
t = Line(C, I)
X_2 = TriangleCenter(A, B, C, 2)
β = Angle(C_a, C, A)
α = Angle(A, B, B_a)
gr: θ * 180 / π
texto1: "\theta = " + (LaTeX[θ]) + "   rad. = " + (LaTeX[gr]) + "°"
J = Intersect(l, h)
K = Intersect(m, g)
d_1 = Line(K, J)
X_4 = TriangleCenter(A, B, C, 4)

Tool: Triangulo Circunceviano (command TrianguloCircunceviano)
Dar ABC y P
Input: L, M, N, P
Output: polígono1, L', M', N'

X3 = TriangleCenter(L, M, N, 3)
e = Line(P, L)
f = OrthogonalLine(X3, e)
L' = Mirror(L, f)
g = Line(P, M)
h = OrthogonalLine(X3, g)
M' = Mirror(M, h)
i = Line(P, N)
j = OrthogonalLine(X3, i)
N' = Mirror(N, j)
polígono1, n', l', m' = Polygon(L', M', N')

Tool: Parabola HG21113 (command ParabolaHG21113)
Dar ABC
Input: A, B, C
Output: p, T_a

polígono1, c, a, b = Polygon(A, B, C)
X_6 = TriangleCenter(A, B, C, 6)
polígono4, D, E, F = TrianguloCircunceviano(A, B, C, X_6)
G = Midpoint(a)
j = Line(A, G)
p = Parabola(D, j)
l = Polar(B, p)
m = Polar(C, p)
T_a = Intersect(m, l)

Tool: Tripolar
Dar los vértices de un triángulo y un punto
Input: A, B, C, P
Output: l

d = Line(B, C)
e = Line(C, A)
f = Line(A, B)
g = Line(P, A)
h = Line(P, B)
i = Line(P, C)
E = Intersect(h, e)
F = Intersect(d, g)
j = Line(E, F)
G = Intersect(f, i)
k = Line(G, F)
H = Intersect(e, k)
I = Intersect(j, f)
l = Line(H, I)