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圆周角舞动

圆周角舞动
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2016-01-22 09:22
圆角变换
所属专题 Circles (Theorems)
这个范例展示了圆周角的动态变化。它涉及圆周角的基本性质，如圆周角等于其所对弧的一半。通过使用GeoGebra命令如Circle、CircumcircleArc、Rotate等，可以直观地观察到圆周角随圆上点移动的变化。适合初中及以上学生学习圆周角的相关概念。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Segment(B, A) → a
  3. Point(c) → C
  4. Segment(A, C) → b
  5. Point(c) → D
  6. CircumcircleArc(C, D, B) → d
  7. CircleArc(A, B, C) → e
  8. Point(d) → E
  9. Segment(C, E) → f
  10. Segment(E, B) → g
  11. Circle(E, 1.5) → h
  12. Ray(E, C) → i
  13. Ray(E, B) → j
  14. Intersect(h, j) → F,
  15. Intersect(h, i) → G,
  16. CircleSector(E, F, G) → k
  17. Segment(E, A) → l
  18. Line(A, xAxis) → m
  19. Dilate(E, If[0 ≤ n ≤ 1, 1 - n, 0], A) → E'
  20. Vector(E, E') → u
  21. Translate(k, u) → k'
  22. Line(E, a) → p
  23. Line(E, b) → q
  24. Intersect(h, p, 1) → H
  25. Angle(H, E, B) → α
  26. Intersect(h, q, 2) → I
  27. Angle(C, E, I) → β
  28. Dilate(E, If[1 < n ≤ 2, 2 - n, 0], A) → E'_1
  29. Vector(E, E'_1) → v
  30. Translate(k, v) → k'_1
  31. Rotate(k'_1, If[1 < n ≤ 2, ((n - 1) * β), β], E'_1) → k''
  32. Rotate(k', If[0 < n ≤ 1, ((-n) * α), (-α)], E') → k''_1
  33. Circle(A, 1.5) → r
  34. Intersect(r, a, 1) → J
  35. Intersect(r, b, 1) → K
  36. CircleSector(A, J, K) → s
  37. Point(d) → L
  38. Point(d) → M
  39. Point(d) → N
  40. Point(d) → O
  41. Point(d) → P
  42. Segment(L, B) → t
  43. Segment(L, C) → a_1
  44. Segment(M, B) → b_1
  45. Segment(M, C) → c_1
  46. Segment(N, B) → d_1
  47. Segment(N, C) → e_1
  48. Segment(O, B) → f_1
  49. Segment(O, C) → g_1
  50. Segment(P, C) → h_1
  51. Segment(P, B) → i_1
  52. Vector(E, L) → w_2
  53. Vector(E, P) → j_1
  54. Circle(L, 1.5) → k_1
  55. Circle(M, 1.5) → p_1
  56. Circle(N, 1.5) → q_1
  57. Circle(O, 1.5) → r_1
  58. Circle(P, 1.5) → s_1
  59. Intersect(k_1, t, 1) → Q
  60. Intersect(k_1, a_1, 1) → R
  61. Intersect(p_1, b_1, 1) → S
  62. Intersect(p_1, c_1, 1) → T
  63. Intersect(q_1, d_1) → U,
  64. Intersect(q_1, e_1, 1) → V
  65. Intersect(r_1, f_1, 1) → W
  66. Intersect(r_1, g_1, 1) → Z
  67. Intersect(s_1, i_1, 1) → A_1
  68. Intersect(s_1, h_1, 1) → B_1
  69. CircleSector(M, S, T) → t_1
  70. CircleSector(L, Q, R) → c_2
  71. CircleSector(N, U, V) → d_2
  72. CircleSector(O, W, Z) → e_2
  73. CircleSector(P, A_1, B_1) → f_2
  74. Dilate(E, If[0 < w < 1, 1 - w, 0], L) → E'_2
  75. Vector(E, E'_2) → l_1
  76. Translate(k, l_1) → k'_2
  77. Line(E, a_1) → m_1
  78. Point(m_1) → C_1
  79. Angle(C, E, C_1) → γ
  80. Rotate(k'_2, If[0 < w < 1, (w * γ), 0], E'_2) → g_2
  81. Dilate(L, If[1 < w < 2, 2 - w, 0], O) → L'
  82. Vector(L, L') → u_1
  83. Line(L, f_1) → n_1
  84. Translate(c_2, u_1) → h_2
  85. Intersect(k_1, n_1, 2) → D_1
  86. Angle(D_1, L, Q) → δ
  87. Rotate(h_2, If[1 < w < 2, ((-(w - 1)) * δ), 0], L') → k_2
  88. Dilate(O, If[2 < w < 3, 3 - w, 0], M) → O'
  89. Vector(O, O') → w_1
  90. Translate(e_2, w_1) → p_2
  91. Line(O, c_1) → a_2
  92. Intersect(r_1, a_2, 2) → E_1
  93. Angle(Z, O, E_1) → ε
  94. Rotate(p_2, If[2 < w < 3, ((w - 2) * ε), 0], O') → q_2
  95. Dilate(M, If[3 < w < 4, 4 - w, 0], P) → M'
  96. Vector(M, M') → v_1
  97. Translate(t_1, v_1) → r_2
  98. Line(M, i_1) → b_2
  99. Intersect(p_1, b_2, 2) → F_1
  100. Angle(S, M, F_1) → ζ
  101. Rotate(r_2, If[3 < w < 4, ((w - 3) * ζ), 0], M') → s_2
  102. Dilate(P, If[4 < w < 5, 5 - w, 0], N) → P'
  103. Vector(P, P') → u_2
  104. Translate(f_2, u_2) → t_2
  105. Line(P, e_1) → i_2
  106. Intersect(s_1, i_2, 2) → G_1
  107. Angle(B_1, P, G_1) → η
  108. Rotate(t_2, If[4 < w < 5, ((w - 4) * η), 0], P') → c_3