Point de Lemoine

Point de Brocard Ω

Point de Brocard Ω'

triangle de Brocard

triangle Ω

Triangle Ω'

Triangle O

triangle C1

triangle C2

triangle C3

inv

tous

A = (1, 6)
C = Point(xAxis)
B = Intersect(xAxis, yAxis)
c_2 = Circle(A, B, C)
h = Tangent(A, c_2)
e = Tangent(C, c_2)
B' = Intersect(e, h)
c_1 = Line(B, B')
O = Center(c_2)
bc = Line(B, C)
ac = Line(C, A)
ab = Line(A, B)
a = Segment(B, C)
b = Segment(C, A)
c = Segment(A, B)
f = Line(A, bc)
D = Intersect(e, f)
g = Segment(D, B)
i = Line(B, b)
E = Intersect(h, i)
j = Segment(E, C)
Ω = Intersect(g, j)
F_1 = Intersect(e, i)
k = Segment(A, F_1)
l = Line(C, c)
F = Intersect(h, l)
m = Segment(B, F)
Ω' = Intersect(k, m)
p = Circle(Ω', Ω, O)
n = Tangent(B, c_2)
C' = Intersect(h, n)
A' = Intersect(e, n)
q = Line(C', C)
r = Line(A, A')
K = Intersect(r, q)
s = OrthogonalLine(O, r)
C_1 = Intersect(s, r)
t_5 = OrthogonalLine(O, q)
C_3 = Intersect(q, t_5)
b_1 = OrthogonalLine(O, c_1)
C_2 = Intersect(b_1, c_1)
a_1 = Segment(O, C_2)
d_1 = Segment(O, C_1)
e_1 = Segment(O, C_3)
f_1 = OrthogonalLine(Ω, a)
g_1 = OrthogonalLine(Ω, b)
h_1 = OrthogonalLine(Ω, c)
A_Ω = Intersect(ab, h_1)
B_Ω = Intersect(bc, f_1)
C_Ω = Intersect(ac, g_1)
d = Segment(Ω, B_Ω)
i_1 = Segment(Ω, C_Ω)
j_1 = Segment(Ω, A_Ω)
k_1 = Segment(A_Ω, C_Ω)
l_1 = Segment(C_Ω, B_Ω)
m_1 = Segment(B_Ω, A_Ω)
cL = false
cB = false
cB' = false
cT = false
tB = false
p_1 = OrthogonalLine(Ω', a)
q_1 = OrthogonalLine(Ω', b)
r_1 = OrthogonalLine(Ω', c)
B_{Ω'} = Intersect(ab, r_1)
A_{Ω'} = Intersect(ac, q_1)
C_{Ω'} = Intersect(bc, p_1)
s_1 = Segment(Ω', C_{Ω'})
t_1 = Segment(Ω', A_{Ω'})
a_2 = Segment(Ω', B_{Ω'})
b_2 = Segment(B_{Ω'}, A_{Ω'})
d_2 = Segment(A_{Ω'}, C_{Ω'})
e_2 = Segment(C_{Ω'}, B_{Ω'})
tB' = false
tO = false
B_O = Midpoint(A, C)
A_O = Midpoint(C, B)
C_O = Midpoint(B, A)
f_2 = Segment(O, B_O)
g_2 = Segment(O, A_O)
h_2 = Segment(O, C_O)
i_2 = Segment(C_O, B_O)
j_2 = Segment(B_O, A_O)
k_2 = Segment(A_O, C_O)
l_2 = OrthogonalLine(C_1, bc)
m_2 = OrthogonalLine(C_1, ab)
n_2 = OrthogonalLine(C_1, ac)
A_{C1} = Intersect(bc, l_2)
C_{C1} = Intersect(ac, n_2)
B_{C1} = Intersect(ab, m_2)
p_2 = Segment(B_{C1}, C_{C1})
q_2 = Segment(C_{C1}, A_{C1})
r_2 = Segment(A_{C1}, B_{C1})
s_2 = Segment(B_{C1}, C_1)
t_2 = Segment(C_1, A_{C1})
a_3 = Segment(C_1, C_{C1})
t1 = true
b_3 = OrthogonalLine(C_2, ac)
c_3 = OrthogonalLine(C_2, bc)
d_3 = OrthogonalLine(C_2, ab)
C_{C2} = Intersect(bc, c_3)
B_{C2} = Intersect(ac, b_3)
A_{C2} = Intersect(ab, d_3)
e_3 = Segment(A_{C2}, B_{C2})
f_3 = Segment(B_{C2}, C_{C2})
g_3 = Segment(C_{C2}, A_{C2})
h_3 = Segment(C_2, B_{C2})
i_3 = Segment(C_2, A_{C2})
j_3 = Segment(C_2, C_{C2})
t2 = false
k_3 = OrthogonalLine(C_3, bc)
l_3 = OrthogonalLine(C_3, ac)
m_3 = OrthogonalLine(C_3, ab)
B_{C3} = Intersect(bc, k_3)
A_{C3} = Intersect(ac, l_3)
C_{C3} = Intersect(ab, m_3)
n_3 = Segment(C_{C3}, A_{C3})
p_3 = Segment(A_{C3}, B_{C3})
q_3 = Segment(B_{C3}, C_{C3})
r_3 = Segment(C_{C3}, C_3)
s_3 = Segment(C_3, A_{C3})
t_3 = Segment(C_3, B_{C3})
t3 = false
Ω_1 = Mirror(Ω, c_2)
n_1 = OrthogonalLine(Ω_1, bc)
a_4 = OrthogonalLine(Ω_1, ab)
b_4 = OrthogonalLine(Ω_1, ac)
A_{Ω1} = Intersect(a_4, ab)
B_{Ω1} = Intersect(n_1, bc)
C_{Ω1} = Intersect(ac, b_4)
c_4 = Segment(C_{Ω1}, B_{Ω1})
d_4 = Segment(B_{Ω1}, A_{Ω1})
e_4 = Segment(C_{Ω1}, A_{Ω1})
f_4 = Segment(B_{Ω1}, Ω_1)
g_4 = Segment(Ω_1, A_{Ω1})
h_4 = Segment(Ω_1, C_{Ω1})
o = false
Ω'_1 = Mirror(Ω', c_2)
i_4 = OrthogonalLine(Ω'_1, ac)
j_4 = OrthogonalLine(Ω'_1, bc)
k_4 = OrthogonalLine(Ω'_1, ab)
A_{Ω'1} = Intersect(i_4, ac)
C_{Ω'1} = Intersect(j_4, bc)
B_{Ω'1} = Intersect(k_4, ab)
l_4 = Segment(A_{Ω'1}, B_{Ω'1})
m_4 = Segment(B_{Ω'1}, C_{Ω'1})
n_4 = Segment(C_{Ω'1}, A_{Ω'1})
p_4 = Segment(Ω'_1, A_{Ω'1})
q_4 = Segment(Ω'_1, C_{Ω'1})
r_4 = Segment(Ω'_1, B_{Ω'1})
C'_1 = Mirror(C_1, c_2)
C'_2 = Mirror(C_2, c_2)
C'_3 = Mirror(C_3, c_2)
s_4 = OrthogonalLine(C'_1, ac)
t_4 = OrthogonalLine(C'_1, ab)
a_5 = OrthogonalLine(C'_1, bc)
B_{C1i} = Intersect(t_4, ab)
C_{C1i} = Intersect(s_4, ac)
A_{C1i} = Intersect(a_5, bc)
b_5 = Segment(A_{C1i}, C_{C1i})
c_5 = Segment(C_{C1i}, B_{C1i})
d_5 = Segment(B_{C1i}, A_{C1i})
e_5 = OrthogonalLine(C'_2, bc)
f_5 = OrthogonalLine(C'_2, ab)
g_5 = OrthogonalLine(C'_2, ac)
B_{C2i} = Intersect(g_5, ac)
A_{C2i} = Intersect(f_5, ab)
C_{C2i} = Intersect(bc, e_5)
h_5 = Segment(A_{C2i}, C_{C2i})
i_5 = Segment(B_{C2i}, A_{C2i})
j_5 = Segment(B_{C2i}, C_{C2i})
k_5 = OrthogonalLine(C'_3, bc)
l_5 = OrthogonalLine(C'_3, ac)
m_5 = OrthogonalLine(C'_3, ab)
C_{C3i} = Intersect(m_5, ab)
A_{C3i} = Intersect(l_5, ac)
B_{C3i} = Intersect(k_5, bc)
n_5 = Segment(C_{C3i}, B_{C3i})
p_5 = Segment(B_{C3i}, A_{C3i})
q_5 = Segment(A_{C3i}, C_{C3i})
t = true
poly1, b_ω, a_ω, c_ω = Polygon(A_Ω, C_Ω, B_Ω)
poly2, c_{ω'}, b_{ω'}, a_{ω'} = Polygon(B_{Ω'}, A_{Ω'}, C_{Ω'})
poly3, a_o, c_o, b_o = Polygon(C_O, B_O, A_O)
poly4, a_{c1}, b_{c1}, c_{c1} = Polygon(B_{C1}, C_{C1}, A_{C1})
poly5, c_{c2}, a_{c2}, b_{c2} = Polygon(A_{C2}, B_{C2}, C_{C2})
poly6, b_{c3}, c_{c3}, a_{c3} = Polygon(C_{C3}, A_{C3}, B_{C3})
poly7, a_{ω1}, b_{ω1}, c_{ω1} = Polygon(B_{Ω1}, C_{Ω1}, A_{Ω1})
poly8, c_{ω'1}, a_{ω'1}, b_{ω'1} = Polygon(A_{Ω'1}, B_{Ω'1}, C_{Ω'1})
poly9, b_{c1i}, c'_1, c_{c1i} = Polygon(C'_1, C_{C1i}, B_{C1i})
poly10, c_{c2i}, c'_2, a_{c2i} = Polygon(C'_2, A_{C2i}, C_{C2i})
poly11, c'_3, b_{c3i}, a_{c3i} = Polygon(B_{C3i}, A_{C3i}, C'_3)
r_5 = Segment(A, Ω)
α = Angle(C, B, Ω)
β = Angle(A, C, Ω)
γ = Angle(B, A, Ω)