Animation

Périmètre

Périmètre d'un triangle

Choisis les longueurs des côtés [AB], [BC] et [AC], puis déplace le curseur.

BC = 6 (slider from 0 to 10, step 0.1)
AB = 4 (slider from 0 to 10, step 0.1)
A = (4.310311904434454, 5.339177034343451)
p = Circle(A, AB)
AC = 3 (slider from 0 to 10, step 0.1)
e = Circle(A, AC)
C = Point(e)
q = Circle(C, BC)
B = Intersect(p, q, 1)
poly1, c, a, b = Polygon(A, B, C)
α = Angle(A, C, B)
β = Angle(B, A, C)
γ = Angle(C, B, A)
A'_1 = Rotate(A, α - 3.141592653589793, C)
B'_1 = Rotate(B, α - 3.141592653589793, C)
C'_1 = Rotate(C, α - 3.141592653589793, C)
poly1'_1, c', a', b' = Polygon(A'_1, B'_1, C'_1)
A'' = Rotate(A'_1, β - 3.141592653589793, A'_1)
B''_1 = Rotate(B'_1, β - 3.141592653589793, A'_1)
C''_1 = Rotate(C'_1, β - 3.141592653589793, A'_1)
poly1'', c'', a'', b'' = Polygon(A'', B''_1, C''_1)
f = Segment(C, A'')
g = Segment(A'', B''_1)
h = -8 (slider from -20 to 150, step 1)
A' = Rotate(A, (h - 10) * (α - 3.141592653589793) / 20, C)
B'_2 = Rotate(B, (h - 10) * (α - 3.141592653589793) / 20, C)
C'_2 = Rotate(C, (h - 10) * (α - 3.141592653589793) / 20, C)
poly1', c'_1, a'_1, b'_1 = Polygon(A', B'_2, C'_2)
D = Rotate(A'_1, (h - 40) * (β - 3.141592653589793) / 20, A'_1)
E = Rotate(B'_1, (h - 40) * (β - 3.141592653589793) / 20, A'_1)
F = Rotate(C'_1, (h - 40) * (β - 3.141592653589793) / 20, A'_1)
poly2, f_1, d_1, e_1 = Polygon(D, E, F)
G = (0, 0)
u = Vector(B, G)
i = Segment(B, B''_1)
B'_3 = Translate(B, Vector[(h - 70) * u / 20])
B'''_1 = Translate(B''_1, Vector[(h - 70) * u / 20])
i' = Segment(B'_3, B'''_1)
k = Circle(G, i)
H, I = Intersect(k, xAxis)
B'''_2 = Translate(B''_1, u)
j = Segment(G, B'''_2)
δ = Angle(I, G, B'''_2)
G'_1 = Rotate(G, -δ, G)
J = Rotate(B'''_2, -δ, G)
j'_1 = Segment(G'_1, J)
G' = Rotate(G, (90 - h) * δ / 10, G)
K = Rotate(B'''_2, (90 - h) * δ / 10, G)
j' = Segment(G', K)
d = Segment(B, C)
B'_4 = Translate(B, Vector[(h - 70) * u / 20])
C'_3 = Translate(C, Vector[(h - 70) * u / 20])
d'_1 = Segment(B'_4, C'_3)
C'_4 = Translate(C, Vector[(h - 70) * u / 20])
A'''_1 = Translate(A'', Vector[(h - 70) * u / 20])
f'_1 = Segment(C'_4, A'''_1)
A'''_2 = Translate(A'', Vector[(h - 70) * u / 20])
B'''_3 = Translate(B''_1, Vector[(h - 70) * u / 20])
g'_1 = Segment(A'''_2, B'''_3)
B' = Translate(B, u)
C'_5 = Translate(C, u)
d' = Segment(B', C'_5)
C' = Translate(C, u)
A'''_3 = Translate(A'', u)
f' = Segment(C', A'''_3)
A''' = Translate(A'', u)
B''' = Translate(B''_1, u)
g' = Segment(A''', B''')
B''_2 = Rotate(B', -δ, G)
M = Rotate(C'_5, -δ, G)
d''_1 = Segment(B''_2, M)
C''_2 = Rotate(C', -δ, G)
N = Rotate(A'''_3, -δ, G)
f''_1 = Segment(C''_2, N)
O = Rotate(A''', -δ, G)
P = Rotate(B''', -δ, G)
g''_1 = Segment(O, P)
B'' = Rotate(B', (90 - h) * δ / 10, G)
Q = Rotate(C'_5, (90 - h) * δ / 10, G)
d'' = Segment(B'', Q)
C'' = Rotate(C', (90 - h) * δ / 10, G)
R = Rotate(A'''_3, (90 - h) * δ / 10, G)
f'' = Segment(C'', R)
S = Rotate(A''', (90 - h) * δ / 10, G)
T = Rotate(B''', (90 - h) * δ / 10, G)
g'' = Segment(S, T)
texte1: "Périmètre du triangle = " + (x(J)) + " cm"