三角形的中心点

三角形的中心点
几何画板及绘图内容加载中,请稍等……
2015-02-25 11:41
本范例展示了三角形的八个中心点,包括重心、垂心等。通过使用GeoGebra命令如Polygon、LineBisector、Circle等,可以直观地理解这些中心点的几何意义。适合初中及以上学生学习三角形的几何性质。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(C, c) → e
  4. OrthogonalLine(B, b) → f
  5. Intersect(d, f) → C_1
  6. LineBisector(b) → h
  7. LineBisector(c) → i
  8. LineBisector(a) → j
  9. Intersect(j, h) → C_2
  10. Circle(C_2, C) → k
  11. AngularBisector(C, B, A) → m
  12. AngularBisector(B, A, C) → n
  13. AngularBisector(A, C, B) → p
  14. Intersect(n, m) → C_3
  15. OrthogonalLine(C_3, a) → q
  16. Intersect(q, a) → G
  17. Circle(C_3, G) → r
  18. Midpoint(b) → H
  19. Midpoint(c) → I
  20. Midpoint(a) → J
  21. Segment(A, J) → s
  22. Segment(C, I) → t
  23. Segment(B, H) → a_1
  24. Intersect(a_1, t) → C_4
  25. Segment(C_2, C_1) → b_1
  26. Line(C, B) → bc
  27. Line(C, A) → ac
  28. Line(A, B) → ab
  29. Intersect(d, bc) → L
  30. Intersect(f, ac) → M
  31. Intersect(ab, e) → N
  32. Segment(A, L) → f_1
  33. Segment(C, N) → g_1
  34. Segment(B, M) → h_1
  35. Polygon(C, B, 3) → poly2, i_1, j_1, k_1, O
  36. Polygon(A, C, 3) → poly3, l_1, m_1, n_1, P
  37. Polygon(B, A, 3) → poly4, p_1, q_1, r_1, Q
  38. Polygon(A, B, 3) → poly5, b_2, c_2, d_2, S
  39. Polygon(B, C, 3) → poly6, e_2, f_2, g_2, T
  40. Polygon(C, A, 3) → poly7, h_2, i_2, j_2, U
  41. Circle(S, B, A) → c_1
  42. Circle(B, T, C) → d_1
  43. Circle(U, A, C) → e_1
  44. LineBisector(r_1) → p_2
  45. LineBisector(q_1) → q_2
  46. Intersect(p_2, q_2) → R
  47. Line(C, R) → s_1
  48. LineBisector(m_1) → t_1
  49. LineBisector(n_1) → a_2
  50. Intersect(t_1, a_2) → A_1
  51. Line(B, A_1) → n_2
  52. LineBisector(k_1) → r_2
  53. LineBisector(j_1) → s_2
  54. Intersect(r_2, s_2) → B_1
  55. Line(A, B_1) → t_2
  56. Intersect(t_2, n_2) → C_7
  57. Circle(B, A, Q) → c_3
  58. Circle(C, A, P) → d_3
  59. Circle(C, B, O) → e_3
  60. Intersect(c_3, e_3) → D_1, C_8, ,
  61. Intersect(c_1, d_1, 2) → C_6
  62. Center(c_1) → W
  63. Center(d_1) → Z
  64. Center(e_1) → F_1
  65. Segment(F_1, B) → k_2
  66. Segment(W, C) → l_2
  67. Segment(A, Z) → m_2
  68. Intersect(m_2, k_2) → C_5
  69. Segment(P_1, P_2) → b_3
  70. Segment(P_2, P_6) → f_3
  71. Line(P_1, P_2) → a_3
  72. Line(P_2, P_8) → g_3
  73. Line(P_2, P_6) → h_3

AI 绘图提示语参考

绘制一个三角形ABC,然后依次画出它的外心、垂心、内心、重心、九点圆的圆心、欧拉线、内切圆的圆心、旁切圆的圆心,并标出这些中心点和它们之间的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。