A = (4.538455357360664, 4.758953074485012)
B = (-1.0472258018537302, -1.4616482254689227)
C = (7.472511047062116, -1.249618417722732)
polígono1, c, a, b = Polygon(A, B, C)
α = Angle(B, A, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
A_b = AKBICH(a, β, B, C)
E = AKBICH(a, γ, C, B)
A_c = Mirror(E, a)
d = Line(C, B)
e = Line(A, C)
f = Line(A, B)
B_c, B_a = Herramienta3(B, C, A)
C_a, C_b = Herramienta3(C, A, B)
ma = LineBisector(B_c, C_b)
mb = LineBisector(C_a, A_c)
mc = LineBisector(A_b, B_a)
M = Intersect(mc, mb)
K_{ca} = TriangleCenter(A, B, C_a, 6)
K_{cb} = TriangleCenter(A, B, C_b, 6)
K_{ba} = TriangleCenter(C, A, B_a, 6)
K_{bc} = TriangleCenter(C, A, B_c, 6)
K_{ab} = TriangleCenter(B, C, A_b, 6)
K_{ac} = TriangleCenter(B, C, A_c, 6)
g: sqrt(a)
h: sqrt((a^(2) - b^(2) + c^(2)) * (a^(6) - 3 * a^(4) * b^(2) - 2 * a^(5) * c - 2 * a * c * (b^(2) - c^(2))^(2) - (b^(2) - c^(2))^(3) + 4 * a^(3) * c * (b^(2) + c^(2)) + 3 * a^(2) * (b^(4) - b^(2) * c^(2))))
hC: sqrt(-4 * a^(2) * b^(2) * (a^(2) + b^(2) - c^(2)) * (a^(2) - 2 * a * b + b^(2) - c^(2)) + (a^(4) - a^(3) * b + 2 * a^(2) * (b^(2) - c^(2)) + (b^(2) - c^(2))^(2) + a * (-b^(3) + b * c^(2)))^(2))
hbc: sqrt((a^(2) + b^(2) - c^(2)) * (-2 * a * b^(5) + b^(6) - 3 * b^(4) * c^(2) - 2 * a * b * (a^(2) - c^(2))^(2) + (a^(2) - c^(2))^(3) + 4 * a * b^(3) * (a^(2) + c^(2)) + 3 * b^(2) * (-a^(2) * c^(2) + c^(4))))
q = Segment(A, C_b)
BI = AngularBisector(C, B, A)
CH = OrthogonalLine(C, c)
D = Intersect(BI, CH)
b_1 = Segment(B, D)
c_1 = Segment(C, D)
a_1 = Segment(A_b, D)
polígono2, c_2, a_b, b_2 = Polygon(A_b, B, C)
AbBC = false
CI = AngularBisector(A, C, B)
BH = OrthogonalLine(B, b)
F = Intersect(BH, CI)
e_1 = Segment(A_c, F)
f_1 = Segment(B, F)
g_1 = Segment(C, F)
polígono3, c_3, a_c, b_3 = Polygon(A_c, B, C)
AcBC = false
AH = OrthogonalLine(A, a)
G = Intersect(AH, CI)
h_1 = Segment(B_c, G)
i_1 = Segment(C, G)
j_1 = Segment(G, A)
AI = AngularBisector(B, A, C)
tBcCA, a_2, b_c, c_4 = Polygon(B_c, C, A)
BcCA = false
H = Intersect(AI, CH)
k = Segment(C, H)
l = Segment(A, H)
j = Segment(B_a, H)
tBaCA, a_3, b_a, c_5 = Polygon(B_a, C, A)
BaCA = false
tCaAB, b_4, c_a, a_4 = Polygon(C_a, A, B)
I = Intersect(BH, AI)
m = Segment(A, I)
n = Segment(B, I)
p = Segment(I, C_a)
CaAB = false
J = Intersect(AH, BH)
tCbAB, b_5, c_b, a_5 = Polygon(C_b, A, B)
r = Segment(C_b, J)
s = Segment(J, A)
t = Segment(J, B)
CbAB = false
i = Segment(A_b, C)
d_1 = Segment(A_c, B)
k_1 = Segment(B_a, C)
l_1 = Segment(B_c, A)
m_1 = Segment(C_a, B)

Tool: Conica Cinco Tangentes (command ConicaCincoTangentes)
Dar las cinco tangentes
Input: t_1, t_2, t_3, t_4, t_5
Output: q, P_1, P_2, P_3, P_4, P_5

K = Intersect(t_1, t_5)
N = Intersect(t_3, t_2)
m = Line(N, K)
O = Intersect(t_2, t_1)
L = Intersect(t_5, t_4)
g = Line(L, O)
W_1 = Intersect(g, m)
M = Intersect(t_4, t_3)
p = Line(M, W_1)
P_1 = Intersect(p, t_1)
k = Line(M, O)
W_2 = Intersect(k, m)
n = Line(L, W_2)
P_2 = Intersect(t_2, n)
i = Line(L, N)
W_3 = Intersect(i, k)
l = Line(K, W_3)
P_3 = Intersect(t_3, l)
f = Line(K, M)
W_4 = Intersect(f, i)
j = Line(O, W_4)
P_4 = Intersect(t_4, j)
W_5 = Intersect(g, f)
h = Line(N, W_5)
P_5 = Intersect(t_5, h)
q = Conic(P_4, P_3, P_2, P_1, P_5)

Tool: AKBICH
Dar seg , angulo y extremos del segmento
Input: a, α, B, C
Output: H

$\mathbf \hat{B}$

$\ell$

$\mathcal C$

A = (4.538455357360664, 4.758953074485012)
C_1 = (-1.0472258018537302, -1.4616482254689227)
a = Segment(A, C_1)
k = Circle(B, a)
i = Segment(B, C)
C' = Rotate(C, α, B)
j = Line(B, C')
s = AngularBisector(C, B, C')
t_4 = OrthogonalLine(C, j)
P = Intersect(s, t_4)
q = LineBisector(i)
M_a = Midpoint(i)
t_2 = Line(M_a, j)
H_c = Intersect(j, t_4)
t_3 = OrthogonalLine(H_c, i)
M = Intersect(j, q)
A'_1 = Mirror(B, M)
c_1 = OrthogonalLine(B, j)
L = Intersect(q, c_1)
t_1 = Line(A'_1, L)
e_1, K, L_1, M_1, N, O = ConicaCincoTangentes(j, q, t_3, t_2, t_1)
f_1, g_1 = Tangent(P, e_1)
r = Ray(B, C')
H = Intersect(r, f_1)

Tool: Herramienta3
Input: A, B, C
Output: A_b, A_c

polígono1, c, a, b = Polygon(A, B, C)
β = Angle(C, B, A)
γ = Angle(A, C, B)
A_b = AKBICH(a, β, B, C)
E = AKBICH(a, γ, C, B)
A_c = Mirror(E, a)