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三角形、外接圆与三角度数的动态演示

三角形、外接圆与三角度数的动态演示
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2017-03-14 10:15
测试改名0圆角几何作图
①本范例动态演示了涉及三角形、外接圆及三角度数的定理；②核心数学概念包括外接圆、角度、相似变换、方程等；③作图要点：使用Line, Rotate, Angle, Ray, Segment, Point, Polygon, Circle, Center, Intersect, CircleArc, Min, CircleSector, Dilate, Vector, Translate等GeoGebra命令构建图形；④适合高中及以上数学学习者和教师用于几何定理的可视化教学与探索。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Segment(A, B) → h
  6. Point(g) → C
  7. Segment(A, C) → i
  8. Segment(C, B) → j
  9. Point(j) → D
  10. Polygon(A, C, D) → poly1, d, a_1, c
  11. Circle(A, D, C) → e
  12. Center(e) → E
  13. Angle(B, A, D) → β
  14. Rotate(B, β / 2, A) → B'_1
  15. Angle(B, A, B'_1) → γ
  16. Ray(A, B'_1) → k
  17. Intersect(e, k, 2) → F
  18. Intersect(j, k) → G
  19. Ray(C, F) → l
  20. Intersect(h, l) → H
  21. Segment(G, H) → m
  22. Segment(D, H) → n
  23. Segment(D, F) → p
  24. Angle(F, D, H) → δ
  25. Angle(F, C, D) → ε
  26. Angle(G, H, D) → ζ
  27. Rotate(D, If[0 < b ≤ 2, (b * π), (2 * π)], E) → D'
  28. CircleArc(E, D, D') → q
  29. Segment(A, D) → r
  30. Segment(A, F) → s
  31. Segment(A, H) → t
  32. Min({r, s, t}) → o
  33. Circle(A, (0.25 * o)) → c_1
  34. Intersect(h, t) → I
  35. Intersect(h, t) → J
  36. Intersect(h, t) → K
  37. Intersect(c_1, s) → L,
  38. Intersect(c_1, h) → M,
  39. CircleSector(A, M, L) → d_1
  40. Dilate(A, If[2 < b ≤ 3, 3 - b, 0], F) → A'
  41. Intersect(l, r) → N
  42. Segment(C, N) → f_1
  43. Min({f_1, p, n, m}) → u
  44. Circle(C, (0.35 * u)) → e_1
  45. Circle(D, (0.35 * u)) → g_1
  46. Segment(A, A') → h_1
  47. Dilate(F, If[3 < b ≤ 4, 4 - b, 0], G) → F'
  48. Segment(F, F') → i_1
  49. Dilate(C, If[4 < b ≤ 5, 5 - b, 0], F) → C'
  50. Segment(C, C') → j_1
  51. Dilate(F, If[5 < b ≤ 6, 6 - b, 0], H) → F'_1
  52. Segment(F, F'_1) → k_1
  53. Intersect(e_1, j_1, 1) → O
  54. Intersect(e_1, j, 1) → P
  55. CircleSector(C, O, P) → p_1
  56. Intersect(g_1, p, 1) → Q
  57. Intersect(g_1, n, 1) → R
  58. CircleSector(D, Q, R) → q_1
  59. Rotate(d_1, If[6 < b ≤ 7, ((b - 6) * γ), γ], A) → r_1
  60. Dilate(D, If[7 < b ≤ 8, 8 - b, 0], F) → D'_1
  61. Dilate(D, If[7 < b ≤ 8, 8 - b, 0], H) → D'_2
  62. Segment(D, D'_1) → l_1
  63. Segment(D, D'_2) → m_1
  64. Dilate(H, If[8 < b ≤ 9, 9 - b, 0], G) → H'
  65. Segment(H, H') → n_1
  66. Line(C, n_1) → s_1
  67. Intersect(e_1, s_1, 2) → S
  68. Angle(O, C, S) → θ
  69. Dilate(C, If[10 < b ≤ 11, 11 - b, 0], H) → C'_1
  70. Vector(C, C'_1) → v
  71. Translate(p_1, v) → t_1
  72. Rotate(t_1, If[11 < b ≤ 12, ((b - 11) * θ), θ], H) → c_2
  73. Line(H, D) → b_1
  74. Dilate(D, If[12 < b ≤ 13, 13 - b, 0], H) → D'_3
  75. Vector(D, D'_3) → w
  76. Translate(q_1, w) → d_2
  77. Rotate(d_2, If[13 < b ≤ 14, ((-(b - 13)) * π), (-π)], H) → e_2