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圆与四边形的动态关系

圆与四边形的动态关系
几何画板及绘图内容加载中，请稍等……
2017-04-15 10:35
圆多边形角变换几何作图
所属专题 Circles (Theorems)
这是一个关于圆与四边形之间动态关系的几何作图。通过旋转、平移和缩放等变换，展示了四边形在圆上的位置变化。核心数学概念包括圆、四边形和角度。使用了Circle、Point、Rotate、Intersect、Dilate等GeoGebra命令。适合初中及以上学生学习几何变换和动态几何。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Rotate(C, 2°, A) → C'
  4. CircleArc(A, C', C) → d
  5. Point(d) → D
  6. CircleArc(A, D, C) → e
  7. Point(e) → E
  8. CircleArc(A, E, C) → f
  9. Point(f) → F
  10. CircleArc(A, F, C) → g
  11. Point(g) → G
  12. Segment(D, E) → b
  13. Segment(E, F) → h
  14. Segment(D, G) → a
  15. Segment(G, F) → i
  16. Circle(F, (0.2 * Distance[A, B])) → k
  17. Circle(E, (0.2 * Distance[A, B])) → p
  18. Circle(G, (0.2 * Distance[A, B])) → q
  19. Circle(D, (0.2 * Distance[A, B])) → r
  20. Intersect(k, i, 1) → H
  21. Intersect(k, h, 1) → I
  22. Intersect(p, h, 1) → J
  23. Intersect(p, b, 1) → K
  24. Intersect(r, a, 1) → L
  25. Intersect(r, b, 1) → M
  26. Intersect(q, a, 1) → N
  27. Intersect(q, i, 1) → O
  28. Circle(A, B) → e_1
  29. Dilate(E, If[0 < j ≤ 1, 1 - j, 0], G) → E'
  30. Vector(E, E') → u
  31. Translate(J, u) → J'
  32. Angle(O, G, J') → α
  33. Ray(D, G) → l
  34. Point(l) → P
  35. Dilate(F, If[2 < j ≤ 3, 3 - j, 0], D) → F'
  36. Vector(F, F') → v
  37. Ray(G, D) → n
  38. Point(n) → Q
  39. Translate(I, v) → I'
  40. Angle(I', D, M) → β
  41. Polygon(G, D, E, F) → poly1, g_2, d_2, e_2, f_2
  42. Ray(F, D) → i_1
  43. Ray(G, E) → j_1
  44. Point(i_1) → R
  45. OrthogonalLine(R, i_1) → l_1
  46. OrthogonalLine(G, j_1) → m_1
  47. Intersect(e_1, m_1) → S, T
  48. Intersect(e_1, l_1) → U, V
  49. Intersect(l_1, j_1) → W
  50. Intersect(i_1, m_1) → Z
  51. Segment(F, W) → n_1
  52. Point(n_1) → A_1
  53. Segment(A_1, Z) → p_1
  54. Segment(W, G) → m
  55. Segment(G, Z) → s
  56. Segment(V, S) → t
  57. Segment(W, Z) → f_1
  58. Line(E, D) → g_1
  59. Line(F, W) → h_1
  60. Intersect(h_1, g_1) → B_1
  61. Line(G, Z) → k_1
  62. Intersect(g_1, k_1) → C_1
  63. Line(V, S) → q_1
  64. Line(W, Z) → r_1
  65. Circle(V, 2) → c_1
  66. Circle(B_1, 2) → d_1
  67. Circle(W, 2) → s_1
  68. Intersect(s_1, r_1, 1) → D_1
  69. Intersect(d_1, g_1, 1) → E_1
  70. Intersect(c_1, q_1, 1) → F_1
  71. Ray(W, D_1) → t_1
  72. Ray(B_1, E_1) → b_1
  73. Ray(V, F_1) → h_2
  74. Segment(V, B_1) → i_2
  75. Segment(B_1, W) → j_2
  76. Min(i_2, j_2) → o
  77. Circle(V, (0.35 * o)) → c_2
  78. Intersect(c_2, h_2, 1) → G_1
  79. Line(W, V) → k_2
  80. Intersect(c_2, k_2, 1) → H_1
  81. Dilate(F, If[0 < j ≤ 1, 1 - j, 0], V) → F'_1
  82. Segment(F, F'_1) → l_2
  83. Dilate(V, If[1 < j ≤ 2, 2 - j, 0], W) → V'
  84. Segment(V, V') → m_2
  85. Dilate(F, If[0 < j ≤ 1, 1 - j, 0], D) → E'_1
  86. Segment(F, E'_1) → n_2
  87. Angle(D, F, V) → γ
  88. Dilate(D, If[1 < j ≤ 2, 2 - j, 0], Z) → D'
  89. Segment(D, D') → p_2
  90. Angle(Z, G, W) → δ
  91. Dilate(G, If[2 < j ≤ 3, 3 - j, 0], S) → G'
  92. Segment(G, G') → q_2
  93. Dilate(G, If[2 < j ≤ 3, 3 - j, 0], E) → G'_1
  94. Segment(G, G'_1) → r_2
  95. Intersect(c_2, k_2) → I_1, J_1
  96. Dilate(E, If[3 < j ≤ 4, 4 - j, 0], W) → E'_2
  97. Dilate(S, If[3 < j ≤ 4, 4 - j, 0], Z) → S'
  98. Segment(E, E'_2) → s_2
  99. Segment(S, S') → t_2
  100. Dilate(S, If[4 < j ≤ 5, 5 - j, 0], V) → S'_1
  101. Segment(S, S'_1) → a_1
  102. Dilate(D, If[5 < j ≤ 6, 6 - j, 0], C_1) → D'_1
  103. Dilate(E, If[5 < j ≤ 6, 6 - j, 0], B_1) → E'_3
  104. Dilate(Z, If[6 < j ≤ 7, 7 - j, 0], W) → Z'
  105. Segment(Z, Z') → a_2
  106. Segment(D, D'_1) → b_2
  107. Segment(E, E'_3) → f_3
  108. Angle(F_1, V, J_1) → ε
  109. Rotate(J_1, If[7 < j ≤ 8, ((-(j - 7)) * ε), (-ε)], V) → K_1
  110. CircleSector(V, G_1, J_1) → c_3
  111. CircleSector(V, K_1, J_1) → d_3
  112. Dilate(V, If[8.5 < j ≤ 9.5, 9.5 - j, 0], B_1) → V'_1
  113. Dilate(B_1, If[9.5 < j ≤ 10.5, 10.5 - j, 0], W) → L_1
  114. Vector(V, V'_1) → w
  115. Translate(d_3, w) → e_3
  116. Vector(B_1, L_1) → u_1
  117. Translate(e_3, u_1) → g_3