cordes

la corde est proportionnelle
au rayon du cercle 

polygones

donc le périmètre du polygone inscrit
est proportionnel au rayon du cercle

Examinons ce qui se passe quand on augmente 
le nombre de côtés du polygone

r = 1 (slider from 0.5 to 5, step 0.1)
r' = 4 (slider from 0.5 to 5, step 0.1)
O = Intersect(xAxis, yAxis)
c = Circle(O, r)
c' = Circle(O, r')
n = 8 (slider from 3 to 64, step 1)
A: (0, r)
A': (0, r')
B = Rotate(A, (2 * π / n))
B' = Rotate(A', (2 * π / n))
AB = Segment(A, B)
A'B' = Segment(A', B')
OA' = Segment(O, A')
OB' = Segment(O, B')
OA = Segment(O, A)
OB = Segment(O, B)
rapportDesRayons: OA' / OA
rapportDesCordes: A'B' / AB
texte1: "\begin{tabular}{|m|m|m|}
	\hline
	OA=" + (LaTeX[OA]) + " & OB=" + (LaTeX[OB]) + " & AB=" + (LaTeX[AB]) + " \\ 
	\hline
	OA'=" + (LaTeX[OA']) + " & OB'=" + (LaTeX[OB']) + " & A'B'=" + (LaTeX[A'B']) + "  \\ 
	\hline 
\end{tabular}"
texte2: "\times " + (LaTeX[rapportDesRayons]) + "↓"
texte3: "↓  \times  " + (LaTeX[rapportDesCordes]) + ""
quotientABOB: AB / OB
quotientABOB': A'B' / OB'
texte9: "\underrightarrow{\times " + (LaTeX[quotientABOB]) + "}"
texte10: "\overrightarrow{\times  " + (LaTeX[quotientABOB']) + "}"
poly, f, g, h, i, j, k, l, m, f_1, h_1, j_1, l_1, n_1, q_1, s_1, a_1, c_1, e_1, g_2, i_2, k_2, m_2, p_2, r_2, t_2, b_2, d_2, e_2, h_3, j_3, l_3, n_3, q_3, r_3, a_3, b_3, c_3, g_4, h_4, i_4, m_4, p_4, r_4, t_4, a_4, d_4, e_4, f_5, g_5, l_5, n_5, q_5, s_5, a_5, c_5, d_5, g_6, i_6, k_6, m_6, n_6, p_6, q_6, b_6, C, D, E, F, G, H, P, R, T, V, Z, B_1, D_1, F_1, H_1, J_1, L_1, N_1, P_1, R_1, T_1, V_1, Z_1, B_2, D_2, E_2, H_2, J_2, L_2, N_2, P_2, Q_2, T_2, U_2, V_2, B_3, C_3, D_3, H_3, J_3, L_3, N_3, O_3, R_3, S_3, T_3, U_3, B_4, D_4, F_4, H_4, J_4, L_4, M_4, P_4, R_4, T_4, V_4, W_4, Z_4, A_5, F_5 = Polygon(A, B, n)
poly', p, q, s, t, a, b, d, e, g_1, i_1, k_1, m_1, p_1, r_1, t_1, b_1, d_1, f_2, h_2, j_2, l_2, n_2, q_2, s_2, a_2, c_2, f_3, g_3, i_3, k_3, m_3, p_3, s_3, t_3, d_3, e_3, f_4, j_4, k_4, l_4, n_4, q_4, s_4, b_4, c_4, h_5, i_5, j_5, k_5, m_5, p_5, r_5, t_5, b_5, e_5, f_6, h_6, j_6, l_6, r_6, s_6, t_6, a_6, c_6, I, J, K, L, M, N, Q, S, U, W, A_1, C_1, E_1, G_1, I_1, K_1, M_1, O_1, Q_1, S_1, U_1, W_1, A_2, C_2, F_2, G_2, I_2, K_2, M_2, O_2, R_2, S_2, W_2, Z_2, A_3, E_3, F_3, G_3, I_3, K_3, M_3, P_3, Q_3, V_3, W_3, Z_3, A_4, C_4, E_4, G_4, I_4, K_4, N_4, O_4, Q_4, S_4, U_4, B_5, C_5, D_5, E_5, G_5 = Polygon(A', B', n)
rapportDespérimètres: poly' / poly
périmètrePoly = Perimeter(poly)
périmètrePoly' = Perimeter(poly')
texte6: "\begin{tabular}{|m|m|}
	\hline
	OA=" + (LaTeX[OA]) + "  & périmètre = " + (LaTeX[périmètrePoly]) + " \\ 
	\hline
	OA'=" + (LaTeX[OA']) + "  & périmètre' =" + (LaTeX[périmètrePoly']) + " \\ 
	\hline 
\end{tabular}"
quotientPeriRayon: périmètrePoly / OA
quotientPeriRayon': périmètrePoly' / OA'
texte11: "\underrightarrow{\times  " + (LaTeX[quotientPeriRayon]) + "}"
texte12: "\overrightarrow{\times  " + (LaTeX[quotientPeriRayon']) + "}"
ra: (r * a)