Euler line

Feuerbach hyperbola

KS(Q_aQ_bQ_c)

KS(P_aP_bP_c)

KS(P_aP_bP_c)

KS(Q_aQ_bQ_c)

A = (-7.366228302886731, -12.067179294858928)
B = (25.0086266739738, -11.878220997328613)
C = (21.130654651015153, 8.391378861520652)
polígono1, c, a, b = Polygon(A, B, C)
X_1 = TriangleCenter(A, B, C, 1)
X_3 = TriangleCenter(A, B, C, 3)
X_4 = TriangleCenter(A, B, C, 4)
X_{21} = TriangleCenter(A, B, C, 21)
e = Line(X_3, X_4)
e_1 = Conic(A, B, C, X_4, X_1)
D = Mirror(X_3, X_{21})
f = Line(X_1, D)
X_{3065} = SegundoPuntoRectaConica(X_1, A, B, C, X_4, f)
g = Circle(X_{3065}, B, C)
Q_a = cuartopunto(B, C, X_{3065}, g, e_1)
h = Circle(X_{3065}, C, A)
Q_b = cuartopunto(X_{3065}, C, A, h, e_1)
k = Circle(X_{3065}, A, B)
Q_c = cuartopunto(X_{3065}, B, A, k, e_1)
polígono2, q_c, q_a, q_b = Polygon(Q_a, Q_b, Q_c)
p_a = rectaEuler(B, X_1, C)
p_b = rectaEuler(C, X_1, A)
p_c = rectaEuler(X_1, A, B)
i = Line(Q_a, p_a)
j = Line(Q_b, p_b)
l = Line(Q_c, p_c)
KSQ = Intersect(j, l)
p = Circle(C, X_1, B)
P_a = cuartopunto(B, C, X_1, p, e_1)
q = Circle(C, X_1, A)
P_b = cuartopunto(A, C, X_1, q, e_1)
r = Circle(A, B, X_1)
P_c = cuartopunto(A, B, X_1, r, e_1)
polígono3, p_1, p_2, p_3 = Polygon(P_c, P_b, P_a)
m = Line(P_a, p_a)
n = Line(P_b, p_b)
s = Line(P_c, p_c)
KSP = Intersect(n, s)

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: Segundo Punto Recta Conica (command SegundoPuntoRectaConica)
Dar ABCDE y recta por A
Input: A0, B0, C0, D0, E0, b
Output: A'

e = Line(A0, C0)
f = Line(B0, E0)
P0 = Intersect(e, f)
g = Line(B0, D0)
Q0 = Intersect(b, g)
h = Line(C0, D0)
i = Line(P0, Q0)
R0 = Intersect(h, i)
j = Line(E0, R0)
A' = Intersect(b, j)

Tool: Perspector Conica (command PerspectorConica)
Dar ABC y una cónica (no necesariamente circunscrita)
Input: A, B, C, d
Output: L

e = Polar(A, d)
f = Polar(B, d)
g = Polar(C, d)
I = Intersect(e, g)
h = Line(B, I)
J = Intersect(e, f)
i = Line(C, J)
L = Intersect(i, h)

Tool: Tripolo
Dar los vértices de un triángulo y una recta
Input: A, B, C, d
Output: N

e = Line(C, B)
f = Line(A, C)
g = Line(A, B)
F = Intersect(d, e)
G = Intersect(f, d)
h = Line(G, B)
j = Line(A, F)
I = Intersect(h, j)
k = Line(I, C)
J = Intersect(k, g)
l = Line(G, J)
M = Intersect(l, e)
m = Line(A, M)
N = Intersect(m, k)

Tool: cuarto punto (command cuartopunto)
Dar ABC y dos cónicas circunscritas
Input: A, B, C, d, h
Output: J

H = PerspectorConica(A, B, C, d)
I = PerspectorConica(A, B, C, h)
i = Line(I, H)
J = Tripolo(A, B, C, i)

Tool: rectaEuler
Dar los vértices de un triángulo
Input: D, E, F
Output: m

G = TriangleCenter(D, E, F, 4)
H = TriangleCenter(D, E, F, 3)
m = Line(H, G)