内切圆扩展 - GoGeometry 动态演示

内切圆扩展 - GoGeometry 动态演示
几何画板及绘图内容加载中,请稍等……
2018-03-25 08:53
这是一个动态可修改的几何问题演示,由 Antonio Gutierrez 提出。该范例展示了内切圆的扩展,涉及三角形和圆的相关概念。通过旋转、角度、线段等 GeoGebra 命令,可以构造出动态的几何图形。适合初中及以上学生和教师使用,帮助理解几何作图和内切圆的相关性质。

GeoGebra 命令及参数

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(A, C) → h
  7. Segment(B, C) → i
  8. Polygon(B, A, C) → t1, c, b, a_1
  9. Angle(C, A, B) → β
  10. Angle(B, C, A) → γ
  11. Rotate(C, β / 2, A) → C'
  12. Angle(C, A, C') → δ
  13. Rotate(A, α / 2, B) → A'_1
  14. Angle(A, B, A'_1) → ε
  15. Rotate(B, γ / 2, C) → B'
  16. Angle(B, C, B') → ζ
  17. Ray(B, A'_1) → j
  18. Ray(A, C') → k
  19. Ray(C, B') → l
  20. Intersect(j, k) → D
  21. Min({i, f, h}) → d
  22. Circle(B, (0.2 * d)) → e
  23. Circle(A, (0.2 * d)) → p
  24. Circle(C, (0.2 * d)) → q
  25. OrthogonalLine(D, f) → m
  26. OrthogonalLine(D, h) → n
  27. OrthogonalLine(D, i) → r
  28. Intersect(m, f) → E
  29. Intersect(n, h) → F
  30. Intersect(r, i) → G
  31. Intersect(e, j, 1) → H
  32. Intersect(p, k, 1) → I
  33. Intersect(p, h, 1) → J
  34. Intersect(e, f, 1) → K
  35. Intersect(q, i) → L,
  36. Intersect(q, l, 1) → M
  37. Rotate(K, If[1 < o ≤ 2, ((o - 1) * ε), ε], B) → K'
  38. Dilate(B, If[0 < o ≤ 1, 1 - o, 0], D) → B'_1
  39. Segment(B, B'_1) → s
  40. CircleSector(B, K, K') → t
  41. Rotate(t, If[3 < o ≤ 4, ((o - 3) * ε), ε], B) → t'
  42. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], D) → A'_2
  43. Segment(A, A'_2) → f_1
  44. Rotate(J, If[5 < o ≤ 6, ((o - 5) * δ), δ], A) → J'
  45. CircleSector(A, J, J') → c_1
  46. Rotate(c_1, If[7 < o ≤ 8, ((o - 7) * δ), δ], A) → d_1
  47. Dilate(C, If[8 < o ≤ 9, 9 - o, 0], D) → C'_1
  48. Segment(C, C'_1) → h_1
  49. Rotate(L, If[9 < o ≤ 10, ((o - 9) * ζ), ζ], C) → L'
  50. CircleSector(C, L, L') → e_1
  51. Rotate(e_1, If[11 < o ≤ 12, ((o - 11) * ζ), ζ], C) → k_1
  52. Dilate(D, If[13 < o ≤ 14, 14 - o, 0], E) → D'
  53. Dilate(D, If[14 < o ≤ 15, 15 - o, 0], F) → D'_1
  54. Dilate(D, If[15 < o ≤ 16, 16 - o, 0], G) → D'_2
  55. Segment(D, D') → i_1
  56. Segment(D, D'_1) → j_1
  57. Segment(D, D'_2) → l_1
  58. Angle(D, E, B) → η
  59. Angle(D, F, A) → θ
  60. Angle(D, G, C) → ι
  61. Angle(E, D, F) → κ
  62. Angle(F, D, G) → λ
  63. Rotate(D, If[17 < o ≤ 18, ((o - 17) * κ), κ], D) → D'_3
  64. Rotate(D', If[17 < o ≤ 18, ((o - 17) * κ), κ], D) → D''
  65. Segment(D'_3, D'') → m_1
  66. Rotate(D'_3, If[18 < o ≤ 19, ((o - 18) * λ), λ], D) → P
  67. Rotate(D'', If[18 < o ≤ 19, ((o - 18) * λ), λ], D) → D'''
  68. Segment(P, D''') → n_1
  69. Rotate(G, If[19 < o ≤ 21, ((o - 19) * π), (2 * π)], D) → G'
  70. CircleArc(D, G, G') → p_1
  71. Circle(D, E) → q_1
  72. Line(G, F) → g_1
  73. Line(B, D) → r_1
  74. Intersect(g_1, r_1) → N
  75. Line(N, A) → s_1
  76. Circle(N, (0.1 * d)) → t_1
  77. Intersect(t_1, s_1) → O, Q
  78. Intersect(t_1, r_1) → R, S
  79. Circle(G, 1) → c_2
  80. Circle(F, 1) → d_2
  81. Intersect(c_2, g_1) → T, U
  82. Intersect(d_2, g_1) → V, W
  83. Ray(F, W) → f_2
  84. Dilate(G, If[22 < o ≤ 23, 23 - o, 0], F) → G'_1
  85. Segment(G, G'_1) → g_2
  86. Dilate(D, If[24 < o ≤ 25, 25 - o, 0], N) → A'_3
  87. Segment(D, A'_3) → h_2
  88. Ray(N, O) → i_2
  89. Dilate(A, If[25 < o ≤ 26, 26 - o, 0], N) → A'_4
  90. Segment(A, A'_4) → j_2
  91. Rotate(O, If[27 < o ≤ 28, ((o - 27) * π / 2), π / 2], N) → O'
  92. CircleSector(N, O, O') → e_2
  93. Rotate(e_2, If[29 < o ≤ 30, ((o - 29) * π / 2), π / 2], N) → k_2

AI 绘图提示语参考

绘制一个三角形ABC,然后构造其内切圆,并通过旋转和缩放等操作,生成一系列与内切圆相关的点和线段,最终形成一个包含多个圆和线段的复杂图形。首先画出三角形ABC,接着构造内切圆,然后通过旋转和缩放生成新的点和线段,最后连接这些点和线段形成最终的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。