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两圆及其外公切线共圆关系的动态演示

两圆及其外公切线共圆关系的动态演示
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2017-06-30 09:45
圆多边形几何作图
该范例演示了两个圆与其外公切线之间的共圆关系。核心数学概念包括圆、切线和共圆性。通过使用GeoGebra命令如Circle、Tangent、Intersect等进行构造。适合初中及以上学生学习圆的性质和共圆性。

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(e, h) → G, L
  9. Intersect(e, g) → H, K
  10. Intersect(e, i) → I
  11. Intersect(c, i) → J, M
  12. Intersect(c, g) → O
  13. Circle(D, 2) → p
  14. Circle(O, 2) → r
  15. Circle(K, 2) → s
  16. Circle(I, 2) → t
  17. Circle(G, 2) → d_1
  18. Circle(J, 2) → e_1
  19. Intersect(e_1, i, 1) → P
  20. Intersect(e_1, i, 2) → Q
  21. Intersect(p, h, 1) → R
  22. Intersect(p, h, 2) → S
  23. Intersect(d_1, h, 1) → V
  24. Intersect(d_1, h, 2) → W
  25. Intersect(s, g, 2) → Z
  26. Intersect(s, g, 1) → A_1
  27. Intersect(r, g, 2) → B_1
  28. Intersect(r, g, 1) → C_1
  29. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  30. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], M) → A'_1
  31. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], O) → A'_3
  32. Angle(A, O, C_1) → α
  33. Angle(A, D, S) → δ
  34. Intersect(t, i, 1) → F_1
  35. Angle(C, I, F_1) → ζ
  36. Angle(C, G, W) → θ_1
  37. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], G) → C'
  38. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], I) → C'_2
  39. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], K) → C'_3
  40. Intersect(i, j) → G_1
  41. Intersect(i, j) → H_1
  42. Line(C, H) → k_1
  43. Intersect(e, ee) → J_1, , ,
  44. Dilate(H, If[8 < k ≤ 9, 9 - k, 0], C) → H'_1
  45. Vector(H, H'_1) → w
  46. Dilate(H, If[11 < k ≤ 12, 12 - k, 0], C) → H'_2
  47. Vector(H, H'_2) → u_1
  48. Segment(A, B) → h_2
  49. Intersect(e, ee, 1) → W_1
  50. CircleArc(A, O, D) → k_2
  51. CircleArc(C, G, H) → p_2
  52. Point(k_2) → Z_1
  53. Point(p_2) → A_2
  54. Segment(A, Z_1) → i_2
  55. Segment(C, A_2) → j_2
  56. OrthogonalLine(Z_1, i_2) → l_2
  57. OrthogonalLine(A_2, j_2) → m_2
  58. Line(D, Z_1) → l
  59. Line(G, A_2) → m
  60. Intersect(h, m_2) → E
  61. Intersect(g, m_2) → F
  62. Intersect(l_2, h) → N
  63. Intersect(g, l_2) → T
  64. Intersect(m, l) → U
  65. Line(H, A_2) → n
  66. Line(O, Z_1) → q
  67. Intersect(n, q) → D_1
  68. Circle(A_2, D_1, Z_1) → c_1
  69. Segment(F, E) → f_1
  70. Segment(T, N) → g_1
  71. LineBisector(A_2, D_1) → h_1
  72. LineBisector(D_1, Z_1) → i_1
  73. Intersect(h_1, i_1) → E_1
  74. Dilate(D, If[0 < k ≤ 1, 1 - k, 0], U) → D'
  75. Segment(D, D') → j_1
  76. Dilate(G, If[0 < k ≤ 1, 1 - k, 0], U) → G'
  77. Segment(G, G') → l_1
  78. Dilate(H, If[1 < k ≤ 2, 2 - k, 0], D_1) → H'
  79. Dilate(O, If[1 < k ≤ 2, 2 - k, 0], D_1) → O'
  80. Segment(O, O') → m_1
  81. Segment(H, H') → n_1
  82. Dilate(E_1, If[3 < k ≤ 4, 4 - k, 0], U) → I_1
  83. Circle(E_1, I_1) → p_1