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多边形顶点上的圆

多边形顶点上的圆
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2015-05-27 12:30
圆多边形向量解析几何几何作图
本范例展示了多边形顶点上的圆。涉及的核心数学概念包括圆、多边形和向量。通过使用GeoGebra命令如Polygon、Point、Circle、Segment、Intersect等，可以构造出多边形及其顶点上的圆。适合初中及以上学生学习几何作图和圆的相关性质。

GeoGebra 命令及参数

  1. Polygon(A, B, C, D) → poly1, a, b, c, d
  2. Polygon(A', B', C', D', E') → poly2, e, f, g, h, i
  3. Polygon(A'', B'', C'', D'', E'', F'') → poly3, j, k, l, m, n, o
  4. Point(a) → E
  5. Circle(A, E) → c_1
  6. Segment(E, A) → a_1
  7. Circle(B, E) → d_1
  8. Intersect(d_1, b, 1) → F
  9. Segment(E, B) → b_1
  10. Segment(B, F) → e_1
  11. Circle(C, F) → f_1
  12. Intersect(f_1, c, 1) → G
  13. Segment(C, F) → g_1
  14. Segment(C, G) → h_1
  15. Circle(D, G) → k_1
  16. Intersect(k_1, d, 1) → H
  17. Segment(G, D) → i_1
  18. Segment(D, H) → j_1
  19. Intersect(c_1, d, 1) → H_1
  20. Segment(A, H_1) → l_1
  21. Point(e) → F'
  22. Circle(A', F') → p_1
  23. Circle(B', F') → q_1
  24. Intersect(q_1, f, 1) → G'
  25. Circle(C', G') → r_1
  26. Intersect(r_1, g, 1) → H'
  27. Circle(D', H') → s_1
  28. Intersect(s_1, h, 1) → I'
  29. Circle(E', I') → t_1
  30. Intersect(t_1, i, 1) → J'
  31. Intersect(p_1, i, 1) → J'_1
  32. Segment(A', F') → m_1
  33. Segment(A', J'_1) → n_1
  34. Segment(F', B') → a_2
  35. Segment(B', G') → b_2
  36. Segment(G', C') → c_2
  37. Segment(H', C') → d_2
  38. Segment(D', H') → e_2
  39. Segment(D', I') → f_2
  40. Segment(E', I') → g_2
  41. Segment(E', J') → h_2
  42. Circle(Intersect[AngularBisector[C, B, A], AngularBisector[D, C, B]], Intersect[OrthogonalLine[Intersect[AngularBisector[C, B, A], AngularBisector[D, C, B]], a], a]) → k_2
  43. Point(j) → G''
  44. Circle(A'', G'') → p_2
  45. Circle(B'', G'') → q_2
  46. Intersect(q_2, k, 1) → H''
  47. Circle(C'', H'') → r_2
  48. Intersect(r_2, l, 1) → I''
  49. Circle(D'', I'') → s_2
  50. Intersect(s_2, m, 1) → J''
  51. Circle(E'', J'') → t_2
  52. Intersect(t_2, n, 1) → K''
  53. Circle(F'', K'') → c_3
  54. Intersect(c_3, o, 1) → L''
  55. Intersect(p_2, o, 1) → L''_1
  56. Segment(A'', G'') → i_2
  57. Segment(A'', L''_1) → j_2
  58. Segment(G'', B'') → l_2
  59. Segment(B'', H'') → m_2
  60. Segment(C'', H'') → n_2
  61. Segment(C'', I'') → a_3
  62. Segment(I'', D'') → b_3
  63. Segment(J'', D'') → d_3
  64. Segment(J'', E'') → e_3
  65. Segment(K'', E'') → f_3
  66. Segment(K'', F'') → g_3
  67. Segment(L'', F'') → h_3