Développement par similitude d'un quadrilatère
Author: Bruno Duchesne

Les points A,B,C et D sont mobiles à souhait. Il suffit de cliquer dessus et de déplacer la souris en maintenant le clic.

A = (0, 0)
B = (3.4999901667201962, 0.2212793028753007)
C = (3.187637990550771, 2.2923443808418735)
D = (0.5563042855888699, 0.9415785468136872)
a: D - A
b: B - A
d: C - D
α = Angle(b, d)
c = Distance(A, B)
e = Distance(A, B)
f = Distance(D, C)
E = Dilate(Rotate[Translate[D, a], α, D], f / e, D)
F = Dilate(Rotate[Translate[C, a], α, D], f / e, D)
g = Segment(D, E)
h = Segment(E, F)
i = Segment(F, C)
j = Segment(D, C)
G, H, k, l, m, n = Similitudequadri(B, C, D, A)
I, J, p, q, r, s = Similitudequadri(D, A, B, C)
K, L, t, a_1, b_1, c_1 = Similitudequadri(C, D, A, B)
M, N, d_1, e_1, f_1, g_1 = Similitudequadri(B, J, I, C)
O, P, h_1, i_1, j_1, k_1 = Similitudequadri(D, C, M, E)
Q, R, l_1, m_1, n_1, p_1 = Similitudequadri(C, I, N, M)
S, T, q_1, r_1, s_1, t_1 = Similitudequadri(B, C, I, J)
U, V, a_2, b_2, c_2, d_2 = Similitudequadri(J, S, T, I)
W, Z, e_2, f_2, g_2, h_2 = Similitudequadri(C, M, E, D)
A_1, B_1, i_2, j_2, k_2, l_2 = Similitudequadri(W, D, E, Z)
C_1, D_1, m_2, n_2, p_2, q_2 = Similitudequadri(B, K, L, A)
E_1, F_1, r_2, s_2, t_2, a_3 = Similitudequadri(M, E, B_1, Q)
G_1, H_1, b_3, c_3, d_3, e_3 = Similitudequadri(C, I, J, B)
I_1, J_1, f_3, g_3, h_3, i_3 = Similitudequadri(T, I, J, S)
K_1, L_1, j_3, k_3, l_3, m_3 = Similitudequadri(I, U, V, T)
M_1, N_1, n_3, p_3, q_3, r_3 = Similitudequadri(T, I, U, V)
O_1, P_1, s_3, t_3, a_4, b_4 = Similitudequadri(T, K_1, L_1, V)
Q_1, R_1, c_4, d_4, e_4, f_4 = Similitudequadri(J, I, T, S)
S_1, T_1, g_4, h_4, i_4, j_4 = Similitudequadri(Q, B_1, F_1, E_1)
U_1, V_1, k_4, l_4, m_4, n_4 = Similitudequadri(M, U, N_1, Q)
W_1, Z_1, p_4, q_4, r_4, s_4 = Similitudequadri(U, V, O_1, N_1)
A_2, B_2, t_4, a_5, b_5, c_5 = Similitudequadri(V, L_1, P_1, O_1)
C_2, D_2, d_5, e_5, f_5, g_5 = Similitudequadri(T, V, L_1, R_1)
E_2, F_2, h_5, i_5, j_5, k_5 = Similitudequadri(T, S, Q_1, R_1)
G_2, H_2, l_5, m_5, n_5, p_5 = Similitudequadri(E, D, W, Z)
I_2, J_2, q_5, r_5, s_5, t_5 = Similitudequadri(E, B_1, A_1, Z)
K_2, L_2, a_6, b_6, c_6, d_6 = Similitudequadri(Q, U_1, F_1, B_1)
M_2, N_2, e_6, f_6, g_6, h_6 = Similitudequadri(B_1, F_1, L_2, K_2)
O_2, P_2, i_6, j_6, k_6, l_6 = Similitudequadri(D, A, C_1, W)
Q_2, R_2, m_6, n_6, p_6, q_6 = Similitudequadri(A, L, D_1, C_1)
S_2, T_2, r_6, s_6, t_6, a_7 = Similitudequadri(C_1, D_1, R_2, Q_2)
U_2, V_2, b_7, c_7, d_7, e_7 = Similitudequadri(B, A, L, G_1)
W_2, Z_2, f_7, g_7, h_7, i_7 = Similitudequadri(B, J, J_1, G_1)
A_3, B_3, j_7, k_7, l_7, m_7 = Similitudequadri(C_1, W, O_2, Q_2)
C_3, D_3, n_7, p_7, q_7, r_7 = Similitudequadri(O_2, Q_2, A_3, B_3)
E_3, F_3, s_7, t_7, a_8, b_8 = Similitudequadri(U_1, F_1, T_1, S_1)
G_3, H_3, c_8, d_8, e_8, f_8 = Similitudequadri(Q, N_1, W_1, U_1)
I_3, J_3, g_8, h_8, i_8, j_8 = Similitudequadri(N_1, O_1, A_2, W_1)
K_3, L_3, k_8, l_8, m_8, n_8 = Similitudequadri(O_1, P_1, B_2, A_2)
M_3, N_3, p_8, q_8, r_8, s_8 = Similitudequadri(V, O_1, P_1, L_1)
O_3, P_3, t_8, a_9, b_9, c_9 = Similitudequadri(G_1, L, V_2, W_2)
Q_3, R_3, d_9, e_9, f_9, g_9 = Similitudequadri(W_2, G_1, L, V_2)
S_3, T_3, h_9, i_9, j_9, k_9 = Similitudequadri(L, V_2, Q_3, R_3)
U_3, V_3, l_9, m_9, n_9, p_9 = Similitudequadri(R_3, Q_3, T_3, S_3)
W_3, Z_3, q_9, r_9, s_9, t_9 = Similitudequadri(G_1, W_2, Z_2, J_1)
A_4, B_4, a_{10}, b_{10}, c_{10}, d_{10} = Similitudequadri(T, R_1, Q_1, S)
C_4, D_4, e_{10}, f_{10}, g_{10}, h_{10} = Similitudequadri(E_2, R_1, Q_1, F_2)
E_4, F_4, i_{10}, j_{10}, k_{10}, l_{10} = Similitudequadri(S, Q_1, D_4, A_4)
G_4, H_4, m_{10}, n_{10}, p_{10}, q_{10} = Similitudequadri(Q_1, F_2, C_4, D_4)
I_4, J_4, r_{10}, s_{10}, t_{10}, a_{11} = Similitudequadri(L_1, M_3, N_3, P_1)
K_4, L_4, b_{11}, c_{11}, d_{11}, e_{11} = Similitudequadri(P_1, N_3, J_4, I_4)
M_4, N_4, f_{11}, g_{11}, h_{11}, i_{11} = Similitudequadri(G_1, J_1, Z_2, W_2)
O_4, P_4, j_{11}, k_{11}, l_{11}, m_{11} = Similitudequadri(A_4, J_1, Z_2, E_4)
Q_4, R_4, n_{11}, p_{11}, q_{11}, r_{11} = Similitudequadri(A_4, D_4, G_4, E_4)
S_4, T_4, s_{11}, t_{11}, a_{12}, b_{12} = Similitudequadri(C_4, D_4, G_4, H_4)
U_4, V_4, c_{12}, d_{12}, e_{12}, f_{12} = Similitudequadri(L, R_3, Q_3, V_2)
W_4, Z_4, g_{12}, h_{12}, i_{12}, j_{12} = Similitudequadri(S_3, R_3, Q_3, T_3)
A_5, B_5, k_{12}, l_{12}, m_{12}, n_{12} = Similitudequadri(U_3, S_3, T_3, V_3)
C_5, D_5, p_{12}, q_{12}, r_{12}, s_{12} = Similitudequadri(Q_2, S_3, U_3, A_3)
E_5, F_5, t_{12}, a_{13}, b_{13}, c_{13} = Similitudequadri(T_3, S_3, U_3, V_3)
G_5, H_5, d_{13}, e_{13}, f_{13}, g_{13} = Similitudequadri(B_5, T_3, V_3, A_5)
I_5, J_5, h_{13}, i_{13}, j_{13}, k_{13} = Similitudequadri(Q_2, A_3, B_3, O_2)
K_5, L_5, l_{13}, m_{13}, n_{13}, p_{13} = Similitudequadri(O_2, B_3, J_5, I_5)
M_5, N_5, q_{13}, r_{13}, s_{13}, t_{13} = Similitudequadri(O_2, I_5, J_5, B_3)
O_5, P_5, a_{14}, b_{14}, c_{14}, d_{14} = Similitudequadri(I_5, K_5, L_5, J_5)
Q_5, R_5, e_{14}, f_{14}, g_{14}, h_{14} = Similitudequadri(L_2, K_2, K_5, N_2)
S_5, T_5, i_{14}, j_{14}, k_{14}, l_{14} = Similitudequadri(N_2, K_5, R_5, Q_5)
U_5, V_5, m_{14}, n_{14}, p_{14}, q_{14} = Similitudequadri(T_5, R_5, Q_5, S_5)
W_5, Z_5, r_{14}, s_{14}, t_{14}, a_{15} = Similitudequadri(K_5, R_5, Q_5, N_2)
A_6, B_6, b_{15}, c_{15}, d_{15}, e_{15} = Similitudequadri(K_5, K_2, L_2, N_2)
C_6, D_6, f_{15}, g_{15}, h_{15}, i_{15} = Similitudequadri(B_1, K_2, L_2, F_1)
E_6, F_6, j_{15}, k_{15}, l_{15}, m_{15} = Similitudequadri(H_4, G_4, T_4, S_4)
G_6, H_6, n_{15}, p_{15}, q_{15}, r_{15} = Similitudequadri(E_4, G_4, T_4, Q_4)
I_6, J_6, s_{15}, t_{15}, a_{16}, b_{16} = Similitudequadri(E_4, Z_2, P_4, Q_4)
K_6, L_6, c_{16}, d_{16}, e_{16}, f_{16} = Similitudequadri(W_2, Z_2, P_4, M_4)
M_6, N_6, g_{16}, h_{16}, i_{16}, j_{16} = Similitudequadri(V_2, W_2, M_4, U_4)
O_6, P_6, k_{16}, l_{16}, m_{16}, n_{16} = Similitudequadri(Q_3, V_2, U_4, Z_4)
Q_6, R_6, p_{16}, q_{16}, r_{16}, s_{16} = Similitudequadri(T_3, Q_3, Z_4, B_5)
S_6, T_6, t_{16}, a_{17}, b_{17}, c_{17} = Similitudequadri(V_3, T_3, B_5, A_5)
U_6, V_6, d_{17}, e_{17}, f_{17}, g_{17} = Similitudequadri(H_5, V_3, A_5, G_5)
W_6, Z_6, h_{17}, i_{17}, j_{17}, k_{17} = Similitudequadri(S_5, Q_5, Z_5, U_5)
A_7, B_7, l_{17}, m_{17}, n_{17}, p_{17} = Similitudequadri(Q_5, N_2, A_6, Z_5)
C_7, D_7, q_{17}, r_{17}, s_{17}, t_{17} = Similitudequadri(N_2, L_2, D_6, A_6)
E_7, F_7, a_{18}, b_{18}, c_{18}, d_{18} = Similitudequadri(L_2, F_1, C_6, D_6)
G_7, H_7, e_{18}, f_{18}, g_{18}, h_{18} = Similitudequadri(U_1, W_1, I_3, G_3)
I_7, J_7, i_{18}, j_{18}, k_{18}, l_{18} = Similitudequadri(W_1, A_2, K_3, I_3)
K_7, L_7, m_{18}, n_{18}, p_{18}, q_{18} = Similitudequadri(A_2, I_4, K_4, K_3)
M_7, N_7, r_{18}, s_{18}, t_{18}, a_{19} = Similitudequadri(I_4, J_4, L_4, K_4)
O_7, P_7, b_{19}, c_{19}, d_{19}, e_{19} = Similitudequadri(M_7, K_4, L_4, N_7)
Q_7, R_7, f_{19}, g_{19}, h_{19}, i_{19} = Similitudequadri(I_4, K_4, L_4, J_4)
S_7, T_7, j_{19}, k_{19}, l_{19}, m_{19} = Similitudequadri(P_1, I_4, J_4, N_3)
U_7, V_7, n_{19}, p_{19}, q_{19}, r_{19} = Similitudequadri(L_1, P_1, N_3, M_3)
W_7, Z_7, s_{19}, t_{19}, a_{20}, b_{20} = Similitudequadri(R_1, L_1, M_3, E_2)
A_8, B_8, c_{20}, d_{20}, e_{20}, f_{20} = Similitudequadri(Q_1, R_1, E_2, F_2)
C_8, D_8, g_{20}, h_{20}, i_{20}, j_{20} = Similitudequadri(D_4, Q_1, F_2, C_4)
E_8, F_8, k_{20}, l_{20}, m_{20}, n_{20} = Similitudequadri(G_4, D_4, C_4, H_4)
G_8, H_8, p_{20}, q_{20}, r_{20}, s_{20} = Similitudequadri(T_4, G_4, H_4, S_4)
I_8, J_8, t_{20}, a_{21}, b_{21}, c_{21} = Similitudequadri(H_6, T_4, S_4, E_6)
K_8, L_8, d_{21}, e_{21}, f_{21}, g_{21} = Similitudequadri(S_4, J_8, I_8, E_6)
M_8, N_8, h_{21}, i_{21}, j_{21}, k_{21} = Similitudequadri(I_8, L_8, K_8, E_6)
O_8, P_8, l_{21}, m_{21}, n_{21}, p_{21} = Similitudequadri(K_8, E_6, M_8, N_8)
Q_8, R_8, q_{21}, r_{21}, s_{21}, t_{21} = Similitudequadri(N_8, M_8, P_8, O_8)
S_8, T_8, a_{22}, b_{22}, c_{22}, d_{22} = Similitudequadri(O_8, P_8, R_8, Q_8)
U_8, V_8, e_{22}, f_{22}, g_{22}, h_{22} = Similitudequadri(Q_8, R_8, T_8, S_8)
W_8, Z_8, i_{22}, j_{22}, k_{22}, l_{22} = Similitudequadri(S_8, T_8, V_8, U_8)
A_9, B_9, m_{22}, n_{22}, p_{22}, q_{22} = Similitudequadri(U_8, V_8, Z_8, W_8)
C_9, D_9, r_{22}, s_{22}, t_{22}, a_{23} = Similitudequadri(W_8, Z_8, B_9, A_9)
E_9, F_9, b_{23}, c_{23}, d_{23}, e_{23} = Similitudequadri(A_9, B_9, D_9, C_9)
G_9, H_9, f_{23}, g_{23}, h_{23}, i_{23} = Similitudequadri(C_9, D_9, F_9, E_9)
I_9, J_9, j_{23}, k_{23}, l_{23}, m_{23} = Similitudequadri(E_9, G_9, H_9, F_9)
K_9, L_9, n_{23}, p_{23}, q_{23}, r_{23} = Similitudequadri(F_9, H_9, J_9, I_9)
M_9, N_9, s_{23}, t_{23}, a_{24}, b_{24} = Similitudequadri(I_9, J_9, L_9, K_9)
O_9, P_9, c_{24}, d_{24}, e_{24}, f_{24} = Similitudequadri(K_9, L_9, N_9, M_9)
Q_9, R_9, g_{24}, h_{24}, i_{24}, j_{24} = Similitudequadri(M_9, N_9, P_9, O_9)
S_9, T_9, k_{24}, l_{24}, m_{24}, n_{24} = Similitudequadri(O_9, P_9, R_9, Q_9)
U_9, V_9, p_{24}, q_{24}, r_{24}, s_{24} = Similitudequadri(Q_9, R_9, T_9, S_9)
W_9, Z_9, t_{24}, a_{25}, b_{25}, c_{25} = Similitudequadri(S_9, T_9, V_9, U_9)
A_{10}, B_{10}, d_{25}, e_{25}, f_{25}, g_{25} = Similitudequadri(U_9, V_9, Z_9, W_9)
C_{10}, D_{10}, h_{25}, i_{25}, j_{25}, k_{25} = Similitudequadri(W_9, Z_9, B_{10}, A_{10})
p_{25} = Semicircle(A, C)

Tool: Similitudequadri
Input: A, B, C, D
Output: E, F, g, i, j, h

a: D - A
b: B - A
d: C - D
α = Angle(b, d)
e = Distance(A, B)
f = Distance(D, C)
E_1 = Dilate(Rotate[Translate[D, a], α, D], f / e, D)
E = Dilate(Rotate[Translate[D, a], α, D], f / e, D)
F = Dilate(Rotate[Translate[C, a], α, D], f / e, D)
g = Segment(D, E)
h = Segment(E, F)
i = Segment(F, C)
j = Segment(D, C)