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两圆外切内切线段关系动态演示

两圆外切内切线段关系动态演示
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2016-12-16 06:18
圆变换几何作图
所属专题 Circles (Theorems)
本范例动态展示了两圆外切和内切时，由切线生成的线段之间的关系。它涉及圆的几何性质和线段长度的比较。通过使用GeoGebra命令如Circle、Tangent、Intersect等，可以直观地观察到不同情况下线段长度的变化。适合初中及以上学生或教师用于教学和学习。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. PointIn(a) → C
  4. Distance(C, c) → b
  5. Circle(C, d) → e
  6. Tangent(c, e) → g, h, i, j
  7. Intersect(c, h) → D
  8. Intersect(c, j) → E, N
  9. Intersect(e, j) → F
  10. Intersect(e, h) → G, L
  11. Intersect(e, g) → H, K
  12. Intersect(e, i) → I
  13. Intersect(c, i) → J, M
  14. Intersect(c, g) → O
  15. Circle(D, 2) → p
  16. Circle(E, 2) → q
  17. Circle(O, 2) → r
  18. Circle(K, 2) → s
  19. Circle(I, 2) → t
  20. Circle(F, 2) → c_1
  21. Circle(G, 2) → d_1
  22. Circle(J, 2) → e_1
  23. Intersect(e_1, i, 1) → P
  24. Intersect(e_1, i, 2) → Q
  25. Intersect(p, h, 1) → R
  26. Intersect(p, h, 2) → S
  27. Intersect(c_1, j, 2) → T
  28. Intersect(c_1, j, 1) → U
  29. Intersect(d_1, h, 1) → V
  30. Intersect(d_1, h, 2) → W
  31. Intersect(s, g, 2) → Z
  32. Intersect(s, g, 1) → A_1
  33. Intersect(r, g, 2) → B_1
  34. Intersect(r, g, 1) → C_1
  35. Intersect(q, j, 2) → D_1
  36. Intersect(q, j, 1) → E_1
  37. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  38. Dilate(A, If[4 < k ≤ 5, 5 - k, 0], M) → A'_1
  39. Dilate(A, If[9 < k ≤ 10, 10 - k, 0], E) → A'_2
  40. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], O) → A'_3
  41. Angle(A, O, C_1) → α
  42. Angle(A, E, E_1) → β
  43. Angle(A, J, Q) → γ
  44. Angle(A, D, S) → δ
  45. Angle(C, K, A_1) → ε
  46. Intersect(t, i, 1) → F_1
  47. Angle(C, I, F_1) → ζ
  48. Angle(C, F, T) → η
  49. Angle(C, G, W) → θ
  50. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], G) → C'
  51. Dilate(C, If[9 < k ≤ 10, 10 - k, 0], F) → C'_1
  52. Dilate(C, If[4 < k ≤ 5, 5 - k, 0], I) → C'_2
  53. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], K) → C'_3
  54. Segment(A, A') → l
  55. Segment(A, A'_1) → m
  56. Segment(A, A'_2) → n
  57. Segment(A, A'_3) → f_1
  58. Segment(C, C') → g_1
  59. Segment(C, C'_1) → h_1
  60. Segment(C, C'_2) → i_1
  61. Segment(C, C'_3) → j_1
  62. Intersect(i, j) → G_1
  63. Intersect(i, j) → H_1
  64. Intersect(h, i) → I_1
  65. Intersect(g, j) → J_1
  66. Intersect(g, i) → K_1
  67. Intersect(h, j) → L_1
  68. Segment(I_1, M) → k_1
  69. Segment(M, I) → l_1
  70. Segment(I, K_1) → m_1
  71. Segment(J_1, E) → n_1
  72. Segment(E, F) → p_1
  73. Segment(F, L_1) → q_1
  74. Dilate(K_1, If[1 < k ≤ 2, 2 - k, 0], M) → M_1
  75. Dilate(M, If[2 < k ≤ 3, 3 - k, 0], I) → M'
  76. Dilate(I, If[3 < k ≤ 4, 4 - k, 0], I_1) → I'
  77. Segment(K_1, M_1) → r_1
  78. Segment(M, M') → s_1
  79. Segment(I, I') → t_1
  80. Midpoint(M, I) → N_1
  81. Rotate(K_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → O_1
  82. Rotate(M_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → P_1
  83. Segment(O_1, P_1) → a_1
  84. Dilate(J_1, If[6 < k ≤ 7, 7 - k, 0], F) → Q_1
  85. Dilate(F, If[7 < k ≤ 8, 8 - k, 0], E) → F'
  86. Dilate(E, If[8 < k ≤ 9, 9 - k, 0], L_1) → E'
  87. Segment(J_1, Q_1) → b_1
  88. Segment(F, F') → f_2
  89. Segment(E, E') → g_2
  90. Midpoint(Q_1, E) → R_1
  91. Rotate(J_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → S_1
  92. Rotate(Q_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → T_1
  93. Segment(S_1, T_1) → h_2