$a^2=x^2+y^2$

$AB^2=AM^2+BN^2

mais ce n'est pas la seule solution
(faire varier k)

$BN^2=AN^2-AB\times BH-GH\times GI+HP^2$

$BN^2=AN^2-2\times AB \times AN + AB^2

$AB^2=AM^2+AN^2-2\times AB \times AN +AB^2$

donc $AM^2+AN^2=2 \times AB\times AN

$AM$

AM

$AM^2$

=

AM

AM

a: 4
B: (0, 0)
A: (a, 0)
poly1, f, g, h, i, C, D = Polygon(A, B, 4)
k = 2 (slider from 1 to 6, step 1)
t: ((2 * a) * k / (k^(2) + 1))
M: (a - t, 0)
poly2, j, l, m, n, E, F = Polygon(A, M, 4)
N: (a - (k * t), 0)
poly3, p, q, r, s, G, H = Polygon(B, N, 4)
poly4, m_1, a_1, c, d, f_1, e = Polygon(M, B, C, D, F, E)
texte12: "sur cette figure on a $AN=" + (LaTeX[k]) + "\times AM"
poly5, b, g_1, h_1, i_1, I, J = Polygon(A, N, 4)
j_1 = Line(B, H)
K, L = Intersect(j_1, poly5)
k_1 = Segment(H, L)
l_1 = Line(G, H)
O, P = Intersect(l_1, poly5)
n_1 = Segment(H, P)
texte5: "posons $AN=" + (LaTeX[k]) + "\times AM$"
texte6: "$AM^2+(" + (LaTeX[k]) + "\times AM)^2=2\times AB\times (" + (LaTeX[k]) + "\times AM)$"
texte7: "$AM^2+( " + (LaTeX[k]) + "\times AM)^2=2 \times " + (LaTeX[k]) + "\times AB \times AM$"
Q = (-4, -14)
R = (-2.477882962502775, -13.998167015702368)
poly6, p_1, q_1, r_1, s_1, S, T = Polygon(Q, R, 4)
u = Vector(Q, R)
poly6' = Translate(poly6, u)
U = (-1.0044135123604767, -13.998167015702368)
v = Vector(R, U)
poly6'' = Translate(poly6', v)
w = Vector(S, R)
poly6''' = Translate(poly6'', w)
u_1 = Vector(T, Q)
poly6''_1 = Translate(poly6', u_1)
V = (5.722294846984798, -12.396569787286827)
W = (5.758414829348471, -13.957290740575585)
Z = (11.060952275036595, -13.97681238599016)
A_1 = (11.060952275036595, -12.396569787286827)
q1, v_1, w_1, z_1, a_2 = Polygon(V, W, Z, A_1)
texte15: "$2\times" + (LaTeX[k]) + "\times AB$"
B_1 = (-4, -18)
C_1 = (-2.4778829625027754, -17.991482771885114)
poly7, t_1, b_1, c_1, d_1, D_1, E_1 = Polygon(B_1, C_1, 4)
e_1 = Vector(B_1, C_1)
poly7' = Translate(poly7, e_1)
u_2 = Vector(B_1, C_1)
poly7'' = Translate(poly7', u_2)
v_2 = Vector(B_1, C_1)
poly7''' = Translate(poly7'', v_2)
w_2 = Vector(B_1, C_1)
q2 = Translate(poly7''', w_2)
V_1 = (5.754326791553108, -16.36853091375737)
W_1 = (5.7904467739167815, -17.929251867046126)
Z_1 = (11.092984219604904, -17.948773512460704)
A_2 = (11.092984219604904, -16.36853091375737)
q1_1, v_3, w_3, z_2, a_3 = Polygon(V_1, W_1, Z_1, A_2)
texte15_1: "$2\times" + (LaTeX[k]) + "\times AB$"
texte19: "2\times " + (LaTeX[k]) + "\times AB"