Effet d'une homothétie sur une figure
Author: H. Abderrahim

Lancer l'animation en cliquant sur le curseur k ou en appuiant sur le bouton en bas à gauche

Effet d'une homothétie sur une figure

H. Abderrahim

A = (11, 3)
B = (12, 3)
C = Midpoint(A, B)
a = LineBisector(A, B)
D = (10.26, 1)
b = LineBisector(A, C)
D'_1 = Mirror(D, b)
E = Point(b)
c = CircumcircleArc(A, E, C)
F = Point(a)
F'_1 = Mirror(F, b)
G = (11.120000000000001, 3.2)
H = Point(b)
I = (11.14, 3.36)
d = Segment(H, I)
I'_1 = Mirror(I, b)
e = Segment(H, I'_1)
f = Segment(I, I'_1)
G'_1 = Mirror(G, b)
J = Intersect(b, f)
K = Point(b)
g = CircumcircleArc(G, K, G'_1)
L = (11, 5)
h = Line(L, b)
M = (10.84, 4.98)
M'_1 = Mirror(M, h)
N = Point(h)
k_3 = CircumcircleArc(M, N, M'_1)
O = Point(h)
u = Vector(N, O)
M' = Translate(M, u)
N' = Translate(N, u)
P = Translate(M'_1, u)
k' = CircumcircleArc(M', N', P)
M''_1 = Mirror(M', b)
N''_1 = Mirror(N', b)
P'_1 = Mirror(P, b)
k''_1 = CircumcircleArc(M''_1, N''_1, P'_1)
poly1, a_1, d_1, d'_2, c_1 = Polygon(A, D, D'_1, C)
Q = Intersect(h, d_1)
R = Midpoint(D, Q)
i = Line(R, h)
S = Point(i)
T = Point(h)
U = (10.583475513428123, -1.0115323854660356)
j = Segment(S, T)
l = Segment(T, U)
m = Line(S, l)
n = Line(U, j)
V = Intersect(m, n)
poly2, t, s, v, u_1 = Polygon(T, S, V, U)
Z = (10.45062437278636, -1.0743567613331828)
p = CircumcircleArc(V, Z, U)
poly3, r, q, t_1, s_1 = Polygon(R, Q, T, S)
R'_1 = Mirror(R, b)
Q'_1 = Mirror(Q, b)
T'_1 = Mirror(T, b)
S'_1 = Mirror(S, b)
poly3'_1, r', q', t', s' = Polygon(R'_1, Q'_1, T'_1, S'_1)
w = Vector(T, S'_1)
T'_2 = Translate(T, w)
S'_2 = Translate(S, w)
V'_1 = Translate(V, w)
U'_1 = Translate(U, w)
poly2'_1, t'_1, s'_1, v', u' = Polygon(T'_2, S'_2, V'_1, U'_1)
V'_2 = Translate(V, w)
Z'_1 = Translate(Z, w)
U'_2 = Translate(U, w)
p'_1 = CircumcircleArc(V'_2, Z'_1, U'_2)
W = Point(poly1)
A_1 = Point(poly1)
b_1 = LineBisector(A_1, W)
e_1 = Line(W, b_1)
f_1 = Line(A_1, b_1)
B_1 = Point(f_1)
g_1 = Line(B_1, a_1)
C_1 = Intersect(e_1, g_1)
D_1 = (10.222906793048976, 3.4354818325434437)
h_1 = Line(C_1, D_1)
i_1 = Line(B_1, h_1)
j_1 = Line(D_1, g_1)
E_1 = Intersect(i_1, j_1)
F_1 = (10.062654028436022, 3.335323854660347)
k_1 = CircumcircleArc(D_1, F_1, E_1)
poly4, w_1, a_2, b_2, c_2 = Polygon(W, A_1, B_1, C_1)
W'_1 = Mirror(W, b)
G_1 = Mirror(A_1, b)
H_1 = Mirror(B_1, b)
I_1 = Mirror(C_1, b)
poly4'_1, w', g_2, h_2, i_2 = Polygon(W'_1, G_1, H_1, I_1)
poly5, b_3, c_3, d_2, e_2 = Polygon(B_1, C_1, D_1, E_1)
J_1 = Mirror(B_1, b)
K_1 = Mirror(C_1, b)
L_1 = Mirror(D_1, b)
M_1 = Mirror(E_1, b)
poly5'_1, j_2, k_2, l_1, m_1 = Polygon(J_1, K_1, L_1, M_1)
N_1 = Mirror(D_1, b)
O_1 = Mirror(F_1, b)
P_1 = Mirror(E_1, b)
p_1 = CircumcircleArc(N_1, O_1, P_1)
k = -1.1 (slider from -2 to 2, step 0.1)
Centre = (8.988359747324742, 2.02695780200224)
A'_1 = Dilate(A, k, Centre)
D' = Dilate(D, k, Centre)
Q_1 = Dilate(D'_1, k, Centre)
C'_1 = Dilate(C, k, Centre)
poly1', a', d'_1, q_1, c'_1 = Polygon(A'_1, D', Q_1, C'_1)
T'_3 = Dilate(T, k, Centre)
S'_3 = Dilate(S, k, Centre)
V'_3 = Dilate(V, k, Centre)
U'_3 = Dilate(U, k, Centre)
poly2', t'_2, s'_2, v'_1, u'_1 = Polygon(T'_3, S'_3, V'_3, U'_3)
T'' = Dilate(T'_3, k, Centre)
S'' = Dilate(S'_3, k, Centre)
V'' = Dilate(V'_3, k, Centre)
U'' = Dilate(U'_3, k, Centre)
R' = Dilate(R, k, Centre)
Q' = Dilate(Q, k, Centre)
T' = Dilate(T, k, Centre)
S' = Dilate(S, k, Centre)
poly3', r'_1, q'_1, t'_3, s'_3 = Polygon(R', Q', T', S')
R_1 = Dilate(R'_1, k, Centre)
S_1 = Dilate(Q'_1, k, Centre)
T_1 = Dilate(T'_1, k, Centre)
U_1 = Dilate(S'_1, k, Centre)
poly6, r_1, s_2, t_2, u_2 = Polygon(R_1, S_1, T_1, U_1)
V_1 = Dilate(T'_2, k, Centre)
W_1 = Dilate(S'_2, k, Centre)
Z_1 = Dilate(V'_1, k, Centre)
A_2 = Dilate(U'_1, k, Centre)
poly7, v_1, w_2, z_1, a_3 = Polygon(V_1, W_1, Z_1, A_2)
B_2 = Dilate(V'_2, k, Centre)
Z'' = Dilate(Z'_1, k, Centre)
C_2 = Dilate(U'_2, k, Centre)
p'' = CircumcircleArc(B_2, Z'', C_2)
A' = Dilate(A, k, Centre)
E' = Dilate(E, k, Centre)
C' = Dilate(C, k, Centre)
k_5 = CircumcircleArc(A', E', C')
F'' = Dilate(F'_1, k, Centre)
F' = Dilate(F, k, Centre)
G' = Dilate(G, k, Centre)
K' = Dilate(K, k, Centre)
D_2 = Dilate(G'_1, k, Centre)
g' = CircumcircleArc(G', K', D_2)
H'_1 = Dilate(H, k, Centre)
I'_2 = Dilate(I, k, Centre)
d' = Segment(H'_1, I'_2)
I' = Dilate(I, k, Centre)
E_2 = Dilate(I'_1, k, Centre)
f' = Segment(I', E_2)
H' = Dilate(H, k, Centre)
F_2 = Dilate(I'_1, k, Centre)
e' = Segment(H', F_2)
G_2 = Dilate(N_1, k, Centre)
H_2 = Dilate(O_1, k, Centre)
I_2 = Dilate(P_1, k, Centre)
f_2 = CircumcircleArc(G_2, H_2, I_2)
J_2 = Dilate(D_1, k, Centre)
K_2 = Dilate(F_1, k, Centre)
L_2 = Dilate(E_1, k, Centre)
p_2 = CircumcircleArc(J_2, K_2, L_2)
W' = Dilate(W, k, Centre)
M_2 = Dilate(A_1, k, Centre)
N_2 = Dilate(B_1, k, Centre)
O_2 = Dilate(C_1, k, Centre)
poly4', w'_1, m_2, n_2, o_2 = Polygon(W', M_2, N_2, O_2)
P_2 = Dilate(W'_1, k, Centre)
Q_2 = Dilate(G_1, k, Centre)
R_2 = Dilate(H_1, k, Centre)
S_2 = Dilate(I_1, k, Centre)
poly8, p_3, q_2, r_2, s_3 = Polygon(P_2, Q_2, R_2, S_2)
T_2 = Dilate(B_1, k, Centre)
U_2 = Dilate(C_1, k, Centre)
V_2 = Dilate(D_1, k, Centre)
W_2 = Dilate(E_1, k, Centre)
poly5', t_3, u_3, v_2, w_3 = Polygon(T_2, U_2, V_2, W_2)
Z_2 = Dilate(J_1, k, Centre)
A_3 = Dilate(K_1, k, Centre)
B_3 = Dilate(L_1, k, Centre)
C_3 = Dilate(M_1, k, Centre)
poly9, z_2, a_4, b_4, c_4 = Polygon(Z_2, A_3, B_3, C_3)
V'_4 = Dilate(V, k, Centre)
Z'_2 = Dilate(Z, k, Centre)
U'_4 = Dilate(U, k, Centre)
p'_2 = CircumcircleArc(V'_4, Z'_2, U'_4)
V' = Dilate(V, k, Centre)
Z' = Dilate(Z, k, Centre)
U' = Dilate(U, k, Centre)
p' = CircumcircleArc(V', Z', U')
M'' = Dilate(M', k, Centre)
N'' = Dilate(N', k, Centre)
P' = Dilate(P, k, Centre)
k'' = CircumcircleArc(M'', N'', P')
M'''_1 = Dilate(M'', k, Centre)
N'''_1 = Dilate(N'', k, Centre)
P''_1 = Dilate(P', k, Centre)
M''' = Dilate(M'', k, Centre)
N''' = Dilate(N'', k, Centre)
P'' = Dilate(P', k, Centre)
D_3 = Dilate(M''_1, k, Centre)
E_3 = Dilate(N''_1, k, Centre)
F_3 = Dilate(P'_1, k, Centre)
d_3 = CircumcircleArc(D_3, E_3, F_3)