Animation

Choisis la longueur du côté puis déplace le curseur.

Périmètre d'un losange

AB = 2.5 (slider from 0 to 6, step 0.1)
A = (-0.4419173223567724, 6.567895383057949)
d = Circle(A, AB)
B = Point(d)
e = Circle(B, AB)
C = Point(d)
D_1 = Midpoint(B, C)
D = Mirror(A, D_1)
a = Segment(A, B)
b = Segment(B, D)
f = Segment(D, C)
g = Segment(C, A)
α = Angle(B, A, C)
D'_1 = Rotate(D, α - 180°, D)
E = Rotate(C, α - 180°, D)
f' = Segment(D'_1, E)
A'_1 = Rotate(A, α - 180°, D)
B'_1 = Rotate(B, α - 180°, D)
h = Segment(E, A'_1)
F = Rotate(A'_1, -α, E)
B''_1 = Rotate(B'_1, -α, E)
i = Segment(E, F)
j = Segment(F, B''_1)
B''' = Rotate(B''_1, α - 180°, F)
k = Segment(F, B''')
l = Segment(B'_1, A'_1)
G = Intersect(xAxis, yAxis)
u = Vector(B, G)
B'_2 = Translate(B, u)
D'_2 = Translate(D, u)
b'_1 = Segment(B'_2, D'_2)
H = Translate(D'_1, u)
E'_1 = Translate(E, u)
f''_1 = Segment(H, E'_1)
E'_2 = Translate(E, u)
F'_1 = Translate(F, u)
i' = Segment(E'_2, F'_1)
F'_2 = Translate(F, u)
I = Translate(B''', u)
k'_1 = Segment(F'_2, I)
m = Segment(G, I)
p = Circle(G, m)
J, P = Intersect(p, xAxis)
β = Angle(I, B'_2, P)
B'' = Rotate(B'_2, β)
D'' = Rotate(D'_2, β)
b'' = Segment(B'', D'')
H'_1 = Rotate(H, β)
L = Rotate(E'_1, β)
f''' = Segment(H'_1, L)
E'' = Rotate(E'_2, β)
M = Rotate(F'_1, β)
i''_1 = Segment(E'', M)
F'' = Rotate(F'_2, β)
I'_1 = Rotate(I, β)
k'' = Segment(F'', I'_1)
t = -44 (slider from -50 to 150, step 0.1)
D'_3 = Rotate(D, (α - 180°) * t / 20, D)
C'_1 = Rotate(C, (α - 180°) * t / 20, D)
n = Segment(D'_3, C'_1)
C' = Rotate(C, (α - 180°) * t / 20, D)
A'_2 = Rotate(A, (α - 180°) * t / 20, D)
q = Segment(C', A'_2)
B'_3 = Rotate(B, (α - 180°) * t / 20, D)
A' = Rotate(A, (α - 180°) * t / 20, D)
r = Segment(B'_3, A')
E'_3 = Rotate(E, -α * (t - 20) / 20, E)
N = Rotate(A'_1, -α * (t - 20) / 20, E)
s = Segment(E'_3, N)
O = Rotate(B'_1, -α * (t - 20) / 20, E)
Q = Rotate(A'_1, -α * (t - 20) / 20, E)
a_1 = Segment(O, Q)
b_1 = Segment(E'_3, F)
c_1 = Segment(B''_1, F)
F'_3 = Rotate(F, (α - 180°) * (t - 40) / 20, F)
R = Rotate(B''_1, (α - 180°) * (t - 40) / 20, F)
d_1 = Segment(F'_3, R)
B' = Translate(B, Vector[(t - 60) * u / 20])
D' = Translate(D, Vector[(t - 60) * u / 20])
b' = Segment(B', D')
K = Translate(D'_1, Vector[(t - 60) * u / 20])
E' = Translate(E, Vector[(t - 60) * u / 20])
f'' = Segment(K, E')
S = Translate(E'_3, Vector[(t - 60) * u / 20])
F'_4 = Translate(F, Vector[(t - 60) * u / 20])
e_1 = Segment(S, F'_4)
F' = Translate(F, Vector[(t - 60) * u / 20])
T = Translate(B''', Vector[(t - 60) * u / 20])
k' = Segment(F', T)
U = Rotate(B'_2, β, G)
V = Rotate(D'_2, β, G)
f_1 = Segment(U, V)
W = Rotate(B'_2, β, G)
Z = Rotate(D'_2, β, G)
g_1 = Segment(W, Z)
A_1 = Rotate(B'_2, β, G)
B_1 = Rotate(D'_2, β, G)
h_1 = Segment(A_1, B_1)
C_1 = Rotate(B'_2, β * (t - 80) / 20, G)
E_1 = Rotate(D'_2, β * (t - 80) / 20, G)
i_1 = Segment(C_1, E_1)
H' = Rotate(H, β * (t - 80) / 20, G)
F_1 = Rotate(E'_1, β * (t - 80) / 20, G)
j_1 = Segment(H', F_1)
G_1 = Rotate(E'_2, β * (t - 80) / 20, G)
H_1 = Rotate(F'_1, β * (t - 80) / 20, G)
i'' = Segment(G_1, H_1)
I_1 = Rotate(F'_2, β * (t - 80) / 20, G)
I' = Rotate(I, β * (t - 80) / 20, G)
k_1 = Segment(I_1, I')
texte3: "Périmètre du losange = " + m + " cm"