A

Relazione tra congruenza di segmenti  e  secondo teorema di Euclide    ( puoi muovere i punti   A  e  D )

2° teorema di Euclide:    h²  = ( a + m ) m = a m + m²    <=>   AD ⊥ BH
dove:  H = medio( A , D ) ,   m = CD / 2 ,  h = b / 2
quindi:    Q_b = 4 h² = 4 a m + 4 m² = 4 R + 4 Q    <=>   AD ⊥ BH

BA ≡ BD  <=>  AD ⊥ BH  <=> 4 R + 4 Q  = Q_b  <=>  Q_{BD} = Q_a + Q_b
quindi:      BA ≡ BD    <=>    (BD) ²  =  a ²  +  b ²

B = (0, 0)
muovi = (3.830366659947592, 4.738261393414082)
B_1 = If(x(muovi) > 0.0 ∧ y(muovi) > 0.0, muovi)
a_1 = Line(B_1, yAxis)
C = Intersect(a_1, xAxis)
A' = Mirror(B, C)
sCA' = Ray(C, A')
c = Segment(B_1, B)
a = Segment(B, C)
b = Segment(C, B_1)
d_2 = Circle(B, B_1)
D = Point(sCA')
e = Segment(C, D)
f = Segment(B_1, D)
poli1, b_1, a_2, c_1 = Polygon(B, C, B_1)
Q_c, s, t, d_1, e_1, F, I = Polygon(B, B_1, 4.0)
Q_b, d, i, j, k, D_1, E = Polygon(B_1, C, 4.0)
Q_a, m_1, n, q, r, G, H_1 = Polygon(C, B, 4.0)
α = Angle(B_1, C, B)
l = Segment(B_1, D)
H = Midpoint(l)
p = Segment(B, H)
J = Midpoint(d)
K = Midpoint(j)
L = Midpoint(k)
N = Midpoint(i)
g = Segment(J, K)
h_1 = Segment(N, L)
M': (x(H), 0.0)
h = Segment(H, M')
m = Segment(C, M')
O: (0.0, -x(D))
P: (x(D), -x(D))
Q_1: (x(M'), -x(M'))
R_1: (x(M'), y(H_1))
S: (x(D), y(H_1))
T: (x(C), -x(M'))
U: (x(C), -x(D))
V: (x(M'), -x(D))
W: (x(D), -x(M'))
R, c_2, h_2, r_1, m' = Polygon(C, H_1, R_1, M')
poli3, m'_1, r_2, s_1, b' = Polygon(M', R_1, S, D)
Z: (0.0, -x(M'))
poli4, g_1, z, t_1, h_3 = Polygon(G, Z, T, H_1)
poli5, z_1, o, u, t_2 = Polygon(Z, O, U, T)
poli6, u_1, v, q_1, t_3 = Polygon(U, V, Q_1, T)
poli7, v_1, p_1, w, q_2 = Polygon(V, P, W, Q_1)
Q, t_4, q_3, r_3, h_4 = Polygon(T, Q_1, R_1, H_1)
poli9, q_4, w_1, s_2, r_4 = Polygon(Q_1, W, S, R_1)