orthotransversal of P wrt ABC

orthotransversal of P wrt DEF

C = (5, 5.1)
B = (8.04, -0.54)
A = (-0.9, -0.32)
K006 = Cubic(A, B, C, 6)
polígono1, c, a, b = Polygon(A, B, C)
d = Circle(A, B, C)
P = Point(K006)
polígono2, D, E, F = TrianguloCircunceviano(A, B, C, P)
e = ortotransversal(A, B, C, P)
f = ortotransversal(D, E, F, P)
X_1 = TriangleCenter(A, B, C, 1)
X_3 = TriangleCenter(A, B, C, 3)
X_4 = TriangleCenter(A, B, C, 4)
X_{46} = TriangleCenter(A, B, C, 46)
X_{90} = TriangleCenter(A, B, C, 90)
X_{155} = TriangleCenter(A, B, C, 155)
X_{254} = TriangleCenter(A, B, C, 254)
X_{371} = TriangleCenter(A, B, C, 371)
X_{372} = TriangleCenter(A, B, C, 372)
X_{485} = TriangleCenter(A, B, C, 485)
X_{486} = TriangleCenter(A, B, C, 486)
X_{487} = TriangleCenter(A, B, C, 487)
X_{488} = TriangleCenter(A, B, C, 488)

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: ortotransversal
DAr ABC y P, construye la recta ortotransversal de P
Input: A, B, C, P
Output: m

e = Segment(P, B)
f = Segment(P, C)
h = OrthogonalLine(P, e)
i = OrthogonalLine(P, f)
k = Line(C, A)
l = Line(A, B)
E = Intersect(h, k)
F = Intersect(i, l)
m = Line(F, E)

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')