Même périmètre ?

Déplacer les points E, B et/ou C.
Comparer le périmètre de la figure bleue avec celui du grand rectangle.
Donner une explication.

Périmètre figure bleue :

Périmètre du grand rectangle :

Explication

O = Intersect(xAxis, yAxis)
B = (-4.9829522752497235, -2.5268146503884563)
c = Circle(O, B)
D = Mirror(B, O)
C = Point(c)
A = Mirror(C, O)
poly1, c', b, c_1, b' = Polygon(A, B, C, D)
a = Segment(B, D)
E = Point(a)
d = OrthogonalLine(E, c')
e = OrthogonalLine(E, b)
E_1 = Intersect(e, b')
F = Intersect(e, b)
G = Intersect(c', d)
H = Intersect(d, c_1)
poly2, d_1, g, b_1, f = Polygon(E, G, B, F)
poly3, d_2, h, b'_1, e_1 = Polygon(E, H, D, E_1)
poly4, d_3, f_1, c_2, h_1 = Polygon(E, F, C, H)
poly5, d_4, g_1, c'_1, e_2 = Polygon(E, G, A, E_1)
i = false
p1: Perimeter[poly2] + Perimeter[poly3]
texte3: " " + p1 + " cm"
p2: Perimeter[poly5] + Perimeter[poly4]
k = false
texte5: " " + (Perimeter[poly1]) + " cm"
j = Line(A, B)
l = Line(B, C)
I = Point(j)
u = Vector(B, I)
J = Point(l)
v = Vector(B, J)
B'_2 = Translate(B, u)
F'_1 = Translate(F, u)
m = Segment(B'_2, F'_1)
H' = Translate(H, Vector[1.5 * u + Vector[E, F]])
D'_1 = Translate(E, Vector[1.5 * u + Vector[E, F]])
n = Segment(H', D'_1)
B'_3 = Translate(B, Vector[2 * u])
C'_1 = Translate(C, Vector[2 * u])
p = Segment(B'_3, C'_1)
q = Segment(C'_1, C)
r = Segment(F, D'_1)
s = Segment(B, B'_3)
G'_1 = Translate(G, v)
B'_4 = Translate(B, v)
g' = Segment(G'_1, B'_4)
E' = Translate(E_1, Vector[1.5 * v + Vector[E, G]])
D' = Translate(E, Vector[1.5 * v + Vector[E, G]])
t = Segment(E', D')
B'_1 = Translate(B, Vector[2 * v])
K = Translate(A, Vector[2 * v])
a_1 = Segment(B'_1, K)
i_1 = Segment(K, A)
j_1 = Segment(D', G)
k_1 = Segment(B'_1, B)
l_1 = Line(O, l)
m_1 = Line(O, g_1)
E'' = Mirror(E', m_1)
D''_1 = Mirror(D', m_1)
t' = Segment(E'', D''_1)
B'' = Mirror(B'_1, m_1)
K'_1 = Mirror(K, m_1)
n_1 = Segment(B'', K'_1)
G'' = Mirror(G'_1, m_1)
L = Mirror(B'_4, m_1)
g'' = Segment(G'', L)
M = Mirror(B'_2, l_1)
F'' = Mirror(F'_1, l_1)
m' = Segment(M, F'')
N = Mirror(B'_3, l_1)
C''_1 = Mirror(C'_1, l_1)
p' = Segment(N, C''_1)
H'' = Mirror(H', l_1)
P = Mirror(D'_1, l_1)
n' = Segment(H'', P)
C'' = Mirror(C'_1, l_1)
C' = Mirror(C, l_1)
q' = Segment(C'', C')
F' = Mirror(F, l_1)
Q = Mirror(D'_1, l_1)
r' = Segment(F', Q)
B'_5 = Mirror(B, l_1)
R = Mirror(B'_3, l_1)
s' = Segment(B'_5, R)
K' = Mirror(K, m_1)
A' = Mirror(A, m_1)
p_1 = Segment(K', A')
D'' = Mirror(D', m_1)
G' = Mirror(G, m_1)
q_1 = Segment(D'', G')
S = Mirror(B'_1, m_1)
B' = Mirror(B, m_1)
r_1 = Segment(S, B')
ex = false