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动态几何问题3

动态几何问题3
几何画板及绘图内容加载中，请稍等……
2017-02-23 04:22
测试改名0向量几何作图
这是一个动态可修改的几何问题示例，由推特用户Antonino Gutierrez发布。该示例展示了三角形中的切线问题。通过使用GeoGebra命令如Ray, Rotate, Angle, Point等，可以动态地探索和理解几何图形的性质。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Ray(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Point(f) → D
  7. Segment(C, D) → h
  8. Segment(A, D) → i
  9. Segment(A, C) → j
  10. Circle(C, 4) → c
  11. Circle(D, 4) → d
  12. Intersect(c, g, 2) → E
  13. Intersect(d, f, 2) → F
  14. Ray(D, F) → k
  15. Ray(C, E) → l
  16. Min({i, j}) → b
  17. Circle(C, (0.15 * b)) → e
  18. Circle(D, (0.15 * b)) → p
  19. Angle(F, D, C) → β
  20. Angle(D, C, E) → γ
  21. Rotate(F, β / 2, D) → F'
  22. Angle(F, D, F') → δ
  23. Rotate(D, γ / 2, C) → D'
  24. Angle(D, C, D') → ε
  25. Ray(C, D') → m
  26. Ray(D, F') → n
  27. Intersect(e, m, 1) → G
  28. Intersect(e, h, 1) → H
  29. Intersect(p, h, 1) → I
  30. CircleSector(C, H, G) → q
  31. CircleSector(D, F, F') → r
  32. Intersect(m, n) → J
  33. OrthogonalLine(J, k) → s
  34. OrthogonalLine(J, l) → t
  35. Intersect(s, k) → K
  36. Intersect(t, l) → L
  37. Circle(J, K) → c_1
  38. Segment(L, K) → f_1
  39. Midpoint(f_1) → M
  40. OrthogonalLine(M, f_1) → g_1
  41. Intersect(c_1, g_1, 2) → N
  42. Segment(N, C) → h_1
  43. Segment(N, D) → i_1
  44. Intersect(f_1, h_1) → O
  45. Segment(L, O) → j_1
  46. Circle(O, j_1) → d_1
  47. Intersect(d_1, f_1, 2) → P
  48. Polygon(A, D, C) → poly1, c_2, a_1, d_2
  49. Angle(J, K, D) → ζ
  50. Angle(C, L, J) → η
  51. Intersect(f_1, i_1) → Q
  52. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  53. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'_1
  54. Segment(A, A') → k_1
  55. Segment(A, A'_1) → l_1
  56. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], J) → C'
  57. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], J) → D'_1
  58. Segment(C, C') → m_1
  59. Segment(D, D'_1) → n_1
  60. Rotate(r, If[2.5 < o ≤ 3.5, ((o - 2.5) * δ), δ], D) → r'
  61. Rotate(q, If[3.5 < o ≤ 4.5, ((o - 3.5) * ε), ε], C) → q'
  62. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], L) → J'
  63. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], K) → J'_1
  64. Segment(J, J'_1) → p_1
  65. Segment(J, J') → q_1
  66. Angle(L, J, K) → θ
  67. Rotate(L, If[6 < o ≤ 7, ((o - 6) * θ), θ], J) → L'
  68. CircleArc(J, L, L') → e_1
  69. Rotate(K, If[7 < o ≤ 8, ((o - 7) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → K'
  70. CircleArc(J, K, K') → r_1
  71. Rotate(N, If[8 < o ≤ 9, ((o - 8) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → N'
  72. CircleArc(J, N, N') → s_1
  73. Rotate(r_1, If[10 < o ≤ 11, ((o - 10) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → t_1
  74. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], D) → N'_1
  75. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], C) → N'_2
  76. Segment(N, N'_1) → b_1
  77. Segment(N, N'_2) → f_2
  78. Dilate(L, If[12 < o ≤ 13, 13 - o, 0], O) → L'_1
  79. Dilate(O, If[13 < o ≤ 14, 14 - o, 0], P) → O'
  80. Segment(L, L'_1) → g_2
  81. Segment(O, O') → h_2
  82. Dilate(P, If[14 < o ≤ 15, 15 - o, 0], Q) → P'
  83. Segment(P, P') → i_2
  84. Dilate(Q, If[15 < o ≤ 16, 16 - o, 0], K) → Q'
  85. Segment(Q, Q') → j_2
  86. Rotate(L, If[17 < o ≤ 18, ((o - 17) * π), π], O) → L'_2
  87. Rotate(L'_1, If[17 < o ≤ 18, ((o - 17) * π), π], O) → R
  88. Segment(L'_2, R) → k_2
  89. Rotate(Q, If[18 < o ≤ 19, ((o - 18) * π), π], Q) → Q'_1
  90. Rotate(Q', If[18 < o ≤ 19, ((o - 18) * π), π], Q) → Q''
  91. Segment(Q'_1, Q'') → l_2
  92. Min(c_2, d_2) → w
  93. Circle(A, (0.15 * w)) → e_2
  94. Segment(A, C) → m_2
  95. Intersect(e_2, m_2) → S,
  96. Segment(A, D) → n_2
  97. Intersect(e_2, n_2) → T,
  98. CircleSector(A, T, S) → p_2