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切线与割线形成的角：你看到了什么？

切线与割线形成的角：你看到了什么？
几何画板及绘图内容加载中，请稍等……
2015-11-22 09:53
圆角几何作图
所属专题 Circles (Theorems)
这个范例演示了切线与割线形成的角。涉及的核心数学概念包括圆的性质、等腰三角形和角度关系。通过使用GeoGebra命令如Circle、Point、Segment、Tangent等，可以动态地探索这些几何元素之间的关系。适合初中及以上学生或教师使用，帮助理解圆的相关性质和几何作图技巧。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(C, A) → a
  4. OrthogonalLine(C, a) → b
  5. Point(b) → E
  6. Tangent(E, c) → l, m
  7. Intersect(c, m) → K
  8. CircleArc(A, C, K) → t
  9. Point(t) → D
  10. Ray(E, D) → d
  11. Ray(E, C) → e
  12. Segment(A, D) → f
  13. Angle(C, A, D) → α
  14. Rotate(C, α / 2, A) → C'
  15. Angle(C, A, C') → β
  16. Circle(A, 1.5) → h
  17. Intersect(h, a, 1) → H
  18. Intersect(h, f, 1) → I
  19. Angle(I, A, H) → γ
  20. CircleArc(A, K, C) → s
  21. Ray(E, D) → n
  22. Intersect(s, n, 1) → F
  23. Segment(A, F) → q
  24. Intersect(h, q, 1) → L
  25. CircleArc(A, F, C) → r
  26. CircleArc(A, D, F) → c_1
  27. CircleArc(A, C, D) → d_1
  28. Angle(F, A, C) → δ
  29. Rotate(F, δ / 2, A) → F'
  30. Angle(F, A, F') → ε
  31. Vector(A, E) → u
  32. Translate(H, u) → H'
  33. Dilate(A, If[1.5 < j < 2.5, 2.5 - j, 0], E) → A'
  34. Vector(A, A') → v
  35. Line(A, n) → a_1
  36. Intersect(h, a_1) → M, N
  37. Angle(a, e) → λ
  38. Ray(E, K) → b_1
  39. Angle(E, D, A) → μ
  40. CircleArc(A, C, K) → t_1
  41. Point(t_1) → O
  42. CircleArc(A, K, C) → c_2
  43. Point(c_2) → P
  44. Segment(O, C) → i_1
  45. Segment(O, F) → j_1
  46. Segment(P, D) → l_1
  47. Segment(P, C) → m_1
  48. Circle(O, 1.5) → g
  49. Circle(P, 1.5) → k
  50. Intersect(g, j_1, 1) → G
  51. Intersect(g, i_1, 1) → J
  52. Intersect(k, l_1, 1) → Q
  53. Intersect(k, m_1, 1) → R
  54. CircleSector(O, G, J) → p
  55. CircleSector(P, R, Q) → e_1
  56. Dilate(O, If[0 < j < 1, 1 - j, 0], P) → O'
  57. Vector(O, O') → w
  58. Translate(p, w) → p'
  59. Line(O, l_1) → i
  60. Intersect(g, i, 2) → S
  61. Angle(J, O, S) → ζ
  62. Rotate(p', If[0 < j < 1, (j * ζ), 0], O') → p''
  63. Vector(O, P) → u_1
  64. Translate(p, u_1) → p'_1
  65. Rotate(p'_1, ζ, P) → f_1
  66. Translate(G, u_1) → G'
  67. Rotate(G', ζ, P) → G''
  68. CircleSector(P, R, G'') → g_1
  69. Dilate(P, If[1.5 < j < 2.5, 2.5 - j, 0], E) → P'
  70. Vector(P, P') → v_1
  71. Translate(g_1, v_1) → h_1
  72. Vector(P, E) → w_1
  73. Translate(G'', w_1) → G'''
  74. Circle(E, 1.5) → k_1
  75. Intersect(k_1, n, 1) → T
  76. Angle(G''', E, T) → η
  77. Translate(g_1, w_1) → p_1
  78. Rotate(p_1, η, E) → q_1
  79. Rotate(h_1, If[1.5 < j < 2.5, ((j - 1.5) * η), 0], P') → r_1