circumcircle

polar circle

$\ell_a$

$\ell_b$

$\ell_c$

Steiner line l_a

Steiner line l_c

Steiner line l_b

C = (5.660388518609482, 4.068105368952145)
B = (9.055723979839504, 0.5998625998943218)
A = (0.1872491335197477, 0.6379930681579808)
k = Circle(A, B, C)
X_5 = TriangleCenter(A, B, C, 5)
X_4 = TriangleCenter(A, B, C, 4)
X_3 = TriangleCenter(A, B, C, 3)
polígono1, c, a, b = Polygon(A, B, C)
D = Midpoint(a)
j = EjeRadical(X_5, D, X_3, A)
E_1, F_1 = Intersect(k, j)
p = Circle(X_4, E_1)
P_1 = Point(p)
polígono2, P_2, P_3, P_4 = TrianguloAnticeviano(A, B, C, P_1)
d = Segment(P_1, P_2)
e = Segment(P_3, P_2)
f = Segment(P_2, P_4)
g = Segment(P_4, P_1)
h = Segment(P_1, P_3)
i = Segment(P_3, P_4)
l_a = RectaSteinerCuadrilatro(f, h, e, g)
l_b = RectaSteinerCuadrilatro(e, g, i, d)
l_c = RectaSteinerCuadrilatro(i, d, f, h)
G = Intersect(l_b, l_c)
NPC = Circle(X_5, D)
q = Circle(D, B)
H = Midpoint(d)
r = Circle(H, P_1)
I = Midpoint(i)
s = Circle(I, P_3)
E = Midpoint(b)
F = Midpoint(c)
t = Circle(E, A)
J = Midpoint(h)
K = Midpoint(P_2, P_4)
c_1 = Circle(K, P_4)
d_1 = Circle(J, P_1)
e_1 = Circle(F, A)
L = Midpoint(e)
M = Midpoint(g)
f_1 = Circle(M, P_1)
g_1 = Circle(L, P_3)
l = false
m = false
n = false

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: Coordenadas Baricentrias (command CoordenadasBaricentrias)
Dar los vértices ABC y un punto P
Input: A, B, C, P
Output: texto2, CoordBaricentricas

q_1 = Segment(B, P)
APB, b_2, a_2, p_4 = Polygon(A, P, B)
e = Line(A, C)
E_1 = Intersect(e, q_1)
CPA, a_1, c_2, p_3 = Polygon(C, P, A)
BPC, c_1, b_1, p_2 = Polygon(B, P, C)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
f = Line(A, B)
r_1 = Segment(P, C)
F_1 = Intersect(f, r_1)
xx = If(Defined[D_1], -BPC, BPC)
yy = If(Defined[E_1], -CPA, CPA)
zz = If(Defined[F_1], -APB, APB)
CoordBaricentricas: {xx, yy, zz}
texto2: "" + CoordBaricentricas + ""

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: Recta SteinerCuadrilatro (command RectaSteinerCuadrilatro)
Dar 4 rectas
Input: a, b, c, d
Output: h

I = Intersect(a, b)
J = Intersect(c, d)
L = Intersect(a, d)
N = Intersect(b, c)
O = Midpoint(J, I)
P = Midpoint(L, N)
h = EjeRadical(O, I, P, N)

Tool: Triangulo Anticeviano (command TrianguloAnticeviano)
Dar ABC y P
Input: A, B, C, P
Output: polígono3, 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)
j = Line(B', C')
k = Line(C', A')
D = Intersect(h, k)
m = Line(A, D)
E = Intersect(m, d)
n = Line(C', E)
A'' = Intersect(g, n)
F = Intersect(g, j)
p = Line(B, F)
G = Intersect(p, e)
q = Line(C', G)
B'' = Intersect(h, q)
r = Line(C, D)
H = Intersect(r, f)
s = Line(A', H)
C'' = Intersect(i, s)
polígono3, c'', a'', b'' = Polygon(A'', B'', C'')