Afficher les plans de base

Afficher le plan de section

Afficher les points A'', ..., I''

Afficher l'angle droit aux bases

Afficher l'angle droit à la section

Afficher M''

Afficher les milieux

Ajuster les tangentes

D = (2, 2)
B = (8, -2)
A = (-2, -2)
L = Midpoint(A, D)
L_1 = Midpoint(A, L)
AB = Line(A, B)
P_1 = Point(AB)
I = Midpoint(A, B)
IL' = Segment(I, L_1)
u = Vector(A, I)
O = Translate(L, u)
J = Translate(O, u)
o = OrthogonalLine(O, AB)
F = Point(o)
v = Ray(O, F)
O' = Point(v)
K = Translate(D, u)
e_t = Line(P_1, K)
AK = Segment(A, K)
E = Intersect(AK, IL')
ε = Conic(I, J, K, L, E)
H, E_1 = Intersect(ε, e_t)
E_2 = Mirror(E_1, O)
e'_t = Line(K, E_2)
P_2 = Intersect(AB, e'_t)
C = Translate(K, u)
c_1 = Segment(A, B)
c_2 = Segment(B, C)
c_3 = Segment(C, D)
c_4 = Segment(D, A)
a_1 = Line(K, L)
P_0 = Intersect(a_1, AB)
b_1 = Line(O, P_0)
AD = Line(A, D)
M = Point(ε)
MO = Segment(M, O)
α = Point(MO)
distanceOα = Distance(O, α)
distanceOM = Distance(O, M)
ε_α = Dilate(ε, distanceOα / distanceOM, O)
OJ_s = Segment(O, J)
α_1 = Intersect(ε_α, OJ_s)
c_α = Circle(O, α_1)
S_α = Intersect(c_α, v)
u_α = Vector(O, α)
T_α = Translate(S_α, u_α)
h_α = Segment(S_α, T_α)
v_α = Segment(T_α, α)
Z_0 = (-4, 18)
v_0 = Line(Z_0, yAxis)
c_z = Circle(Z_0, 1)
plan_b = true
plan_s = true
seconde = true
angle_b = true
angle_s = true
M_s = true
IaL = false
h_0 = Line(Z_0, xAxis)
Z'_1, Z_1 = Intersect(c_z, v_0)
z_v = Vector(Z_0, Z_1)
h_1 = Translate(h_0, z_v)
c'_z = Circle(Z_0, 6)
Z'_2, Z_2 = Intersect(c'_z, h_0)
z_h = Vector(Z_0, Z_2)
v_1 = Translate(v_0, z_h)
v_2 = Translate(v_1, z_h)
h_2 = Translate(h_1, z_v)
v_3 = Translate(v_2, z_h)
v'_O = Vector(O, O')
A' = Translate(A, v'_O)
I' = Translate(I, v'_O)
B' = Translate(B, v'_O)
J' = Translate(J, v'_O)
C' = Translate(C, v'_O)
K' = Translate(K, v'_O)
D' = Translate(D, v'_O)
L' = Translate(L, v'_O)
M' = Translate(M, v'_O)
α' = Translate(α, v'_O)
ε' = Translate(ε, v'_O)
G = Midpoint(O, O')
S'_α = Mirror(S_α, G)
T'_α = Translate(S'_α, u_α)
E'_1 = Translate(E_1, v'_O)
E'_2 = Translate(E_2, v'_O)
v_g = Segment(E_1, E'_1)
v_d = Segment(E_2, E'_2)
c'_1 = Segment(A', B')
c'_2 = Segment(B', C')
c'_3 = Segment(C', D')
c'_4 = Segment(D', A')
h'_α = Segment(S'_α, T'_α)
v'_α = Segment(T'_α, α')
O'M' = Segment(O', M')
p_1 = OrthogonalLine(E_1, AB)
P'_1 = Intersect(p_1, AB)
t_1 = Tangent(E_1, ε)
P''_1 = Intersect(t_1, AB)
p_2 = OrthogonalLine(E_2, AB)
P'_2 = Intersect(p_2, AB)
t_2, t'_2 = Tangent(E_2, ε)
P''_2 = Intersect(t_2, AB)
distanceP'1P''1 = Distance(P'_1, P''_1)
TexteP'1P''1: "" + (Name[P'_1]) + (Name[P''_1]) + " = " + (Distance[P'_1, P''_1])
distanceP'2P''2 = Distance(P'_2, P''_2)
TexteP'2P''2: "" + (Name[P'_2]) + (Name[P''_2]) + " = " + (Distance[P'_2, P''_2])
h_3 = Translate(h_2, z_v)
h_4 = Translate(h_3, z_v)
tan = false
text1: "(Faire glisser " + (Name[P_1]) + " pour amener " + (Name[P'_1]) + " sur " + (Name[P''_1]) + ".)"
P_3 = Mirror(P_2, P_1)
P_4 = Mirror(P_1, P_2)
s_c = Segment(P_1, P_2)
s_g = Ray(P_1, P_3)
s_d = Ray(P_2, P_4)
P_c = Point(s_c)
b_c = Line(P_c, AD)
I_c = Intersect(b_c, b_1)
a_c = Line(I_c, a_1)
P'_c = Intersect(a_c, AD)
e_c = Line(P_c, K)
e'_c = Line(I, P'_c)
E_c = Intersect(e_c, e'_c)
ε_c = Locus(E_c, P_c)
P_g = Point(s_g)
b_g = Line(P_g, AD)
I_g = Intersect(b_g, b_1)
a_g = Line(I_g, a_1)
P'_g = Intersect(a_g, AD)
e_g = Line(P_g, K)
e'_g = Line(I, P'_g)
E_g = Intersect(e_g, e'_g)
ε_g = Locus(E_g, P_g)
P_d = Point(s_d)
b_d = Line(P_d, AD)
I_d = Intersect(b_1, b_d)
a_d = Line(I_d, a_1)
P'_d = Intersect(AD, a_d)
e_d = Line(P_d, K)
e'_d = Line(P'_d, I)
E_d = Intersect(e_d, e'_d)
ε_d = Locus(E_d, P_d)
O'' = Point(v)
v''_O = Vector(O, O'')
k'': Distance[O, O''] / Distance[O, O']
A'' = Translate(A, v''_O)
I'' = Translate(I, v''_O)
B'' = Translate(B, v''_O)
J'' = Translate(J, v''_O)
C'' = Translate(C, v''_O)
K'' = Translate(K, v''_O)
D'' = Translate(D, v''_O)
L'' = Translate(L, v''_O)
M'' = Translate(M, v''_O)
α'' = Translate(α, v''_O)
S''_α = Translate(S_α, v''_O)
T''_α = Translate(T_α, v''_O)
c''_1 = Segment(A'', B'')
c''_2 = Segment(B'', C'')
c''_3 = Segment(C'', D'')
c''_4 = Segment(D'', A'')
O''M'' = Segment(O'', M'')
h''_α = Segment(S''_α, T''_α)
v''_α = Segment(T''_α, α'')
E''_c = Translate(E_c, v''_O)
E''_g = Translate(E_g, v''_O)
E''_d = Translate(E_d, v''_O)
ε''_c = Locus(E''_c, P_c)
ε''_g = Locus(E''_g, P_g)
ε''_d = Locus(E''_d, P_d)