Homothetie
Author: Gilles Coulombe

Cliquer et glisser le curseur k

A_1 = (-4, 1.92)
O_1 = (-11.52, -1.56)
k = -0.5 (slider from -3 to 3, step 0.5)
A = (-9.04362490223158, -7.077520683893027)
B = Point(Circle[A, 3])
a = Segment(A, B)
b = OrthogonalLine(B, a)
c = Circle(B, 4)
C = Intersect(c, b, 2)
d = Segment(A, C)
e = Segment(C, B)
poly1, c_1, a_1, b_1 = Polygon(A, B, C)
O = (-13.653929358325733, -4.909579897991606)
A' = Dilate(A, k, O)
B' = Dilate(B, k, O)
C' = Dilate(C, k, O)
poly1', c', a', b' = Polygon(A', B', C')
f = Segment(O, C')
g = Segment(O, B')
h = Segment(O, A')
i = Segment(O, C)
j = Segment(O, B)
l = Segment(O, A)
A_2 = (-9.208278632806369, -0.4639291724722372)
O_2 = (-14.641851741774481, -3.7021192071098055)
A'_1 = Dilate(A_2, 2, O_2)
d_1 = Segment(O_2, A'_1)
g_1 = Segment(O_2, A_2)
q_1: d_1 / g_1
texte2_1: "OA = " + g_1 + ""
D_1 = Midpoint(O_2, A_2)
texte3_1: "OA' = " + d_1 + ""
q: c' / c_1
texte2: "Rapport  côtés = A'C' / AC = \frac{" + (LaTeX[b']) + "}{" + (LaTeX[b_1]) + "} = " + (LaTeX[q]) + "   "
texte3: "Rapport   côtés = B'C' / BC =\frac{" + (LaTeX[a']) + "}{" + (LaTeX[a_1]) + "} =  " + (LaTeX[q]) + "  "
A_3 = (-47.29508508169354, 8.744897004787354)
B_1 = Point(Circle[A_3, 3])
a_2 = Segment(A_3, B_1)
b_2 = OrthogonalLine(B_1, a_2)
c_2 = Circle(B_1, 4)
C_1 = Intersect(c_2, b_2, 2)
d_2 = Segment(A_3, C_1)
e_1 = Segment(C_1, B_1)
poly1_1, c_3, a_3, b_3 = Polygon(A_3, B_1, C_1)
O_3 = (-51.9053895377877, 10.912837790688773)
A'_2 = Dilate(A_3, k, O_3)
B'_1 = Dilate(B_1, k, O_3)
C'_1 = Dilate(C_1, k, O_3)
poly1'_1, c'_1, a'_1, b'_1 = Polygon(A'_2, B'_1, C'_1)
f_1 = Segment(O_3, C'_1)
g_2 = Segment(O_3, B'_1)
h_1 = Segment(O_3, A'_2)
i_1 = Segment(O_3, C_1)
j_1 = Segment(O_3, B_1)
l_1 = Segment(O_3, A_3)
q_2: c'_1 / c_3
texte1_1: "Rapport   côtés = A'B' / AB = \frac{" + (LaTeX[c'_1]) + "}{" + (LaTeX[c_3]) + "} =  " + (LaTeX[q_2]) + " "