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等腰三角形的外接圆动画

等腰三角形的外接圆动画
几何画板及绘图内容加载中，请稍等……
2016-10-09 12:16
测试改名0圆变换几何作图滑块动画
这个范例演示了等腰三角形的外接圆动画。涉及的核心数学概念包括等腰三角形的性质、外接圆、对称性等。作图要点包括使用Circle命令绘制圆，使用Intersect命令求交点，使用Dilate和Rotate命令进行变换，使用Segment命令绘制线段。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Circle(A, B_1) → c
  2. Intersect(c, q) → O, P_1
  3. CircleArc(A, O, P_1) → d
  4. Point(d) → C
  5. LineBisector(C, A) → i_1
  6. Segment(A, C) → b
  7. Point(b) → Q
  8. LineBisector(A, Q) → n_1
  9. Segment(A, Q) → n
  10. CircleArc(A, C, P_1) → e
  11. Point(e) → B
  12. LineBisector(A, B) → h_1
  13. Intersect(h_1, i_1) → U
  14. Circle(B, n) → t
  15. Segment(B, A) → g
  16. Intersect(t, g) → P,
  17. LineBisector(A, P) → r_1
  18. Intersect(r_1, n_1) → V
  19. Angle(A, V, U) → δ
  20. Dilate(V, If[12 < j ≤ 13, 13 - j, 0], A) → V'
  21. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
  22. Segment(A, A') → a
  23. Angle(C, A, B) → α
  24. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
  25. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
  26. Segment(A'_1, A'') → a'
  27. Segment(C, B) → f
  28. Midpoint(f) → E
  29. Segment(A, E) → h
  30. Midpoint(h) → F
  31. Segment(A, F) → i
  32. Segment(F, E) → k
  33. Circle(A, (0.35 * i)) → p
  34. Circle(E, (0.15 * Distance[B, E])) → r
  35. Intersect(r, f, 2) → G
  36. Intersect(r, h, 1) → H
  37. Intersect(r, f, 1) → I
  38. Intersect(p, b, 1) → J
  39. Intersect(p, h, 1) → K
  40. Intersect(p, g, 1) → L
  41. Circle(A, B_1) → c_1
  42. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], B) → C'
  43. Segment(C, C') → l
  44. Polygon(C, B, A) → poly1, a_1, c_2, d_1
  45. Circle(C, (0.2 * Distance[B, E])) → e_1
  46. Intersect(e_1, b) → M,
  47. Intersect(e_1, f) → N,
  48. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
  49. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
  50. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], B) → E'
  51. Rotate(E, If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E'_1
  52. Rotate(E', If[7 < j ≤ 8, ((j - 7) * π), 3.141592653589793], E) → E''
  53. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], B) → C'_1
  54. Vector(C, C'_1) → u
  55. Angle(E, C, A) → β
  56. Segment(C, B) → m
  57. Intersect(t, c, 1) → R
  58. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], Q) → A'_3
  59. Segment(A, A'_3) → s
  60. Dilate(A, If[5 < j ≤ 6, 6 - j, 0], B) → A'_4
  61. Vector(A, A'_4) → v
  62. Translate(A, v) → A'_5
  63. Translate(A'_3, v) → D
  64. Segment(A'_5, D) → s'
  65. Line(C, A) → f_1
  66. Line(B, f_1) → g_1
  67. Point(g_1) → S
  68. Angle(A, B, S) → γ
  69. Rotate(A'_5, If[6 < j ≤ 7, ((-(j - 6)) * γ), (-γ)], B) → T
  70. Rotate(D, If[6 < j ≤ 7, ((-(j - 6)) * γ), (-γ)], B) → D'
  71. Segment(T, D') → s''
  72. Dilate(U, If[7 < j ≤ 8, 8 - j, 0], B) → U'
  73. Segment(U, U') → j_1
  74. Rotate(B, If[8 < j ≤ 9, (((j - 8) * 2) * π), (2 * π)], U) → B'
  75. Rotate(U, If[8 < j ≤ 9, (((j - 8) * 2) * π), (2 * π)], U) → U'_1
  76. Rotate(U', If[8 < j ≤ 9, (((j - 8) * 2) * π), (2 * π)], U) → U''
  77. Segment(U'_1, U'') → k_1
  78. CircleArc(U, B, B') → p_1
  79. Polygon(Q, P, A) → poly2, a_2, q_1, p_2
  80. Polygon(C, B, P, Q) → poly3, c_3, b_1, p_3, q_2
  81. Dilate(Q, If[9 < j ≤ 10, 10 - j, 0], P) → Q'
  82. Segment(Q, Q') → l_1
  83. Dilate(P, If[10 < j ≤ 11, 11 - j, 0], A) → P'
  84. Segment(P, P') → m_1
  85. Segment(V, V') → s_1
  86. Rotate(A, If[13 < j ≤ 14, (((j - 13) * 2) * π), (2 * π)], V) → A'_6
  87. Rotate(V, If[13 < j ≤ 14, (((j - 13) * 2) * π), (2 * π)], V) → V'_1
  88. Rotate(V', If[13 < j ≤ 14, ((j - 13) * δ), δ], V) → V''
  89. Segment(V'_1, V'') → t_1
  90. Circle(U, B) → e_2
  91. Circle(V, P) → f_2
  92. CircleArc(V, A, V'') → d_2
  93. Rotate(U_3, If[14 < j ≤ 15, ((j - 14) * ((2 * π) - δ)), (2 * π) - δ], V) → W
  94. CircleArc(V, U_3, W) → g_2
  95. Rotate(V'_1, If[14 < j ≤ 15, ((j - 14) * ((2 * π) - δ)), (2 * π) - δ], V) → Z
  96. Rotate(V'', If[14 < j ≤ 15, ((j - 14) * ((2 * π) - δ)), (2 * π) - δ], V) → V'''
  97. Segment(Z, V''') → h_2