积极 AI Logo 积极 AI

欧拉线与三角形中心

欧拉线与三角形中心
几何画板及绘图内容加载中，请稍等……
2017-01-27 22:33
测试改名0圆向量解析几何几何作图
①本范例演示了三角形欧拉线及其上的五个重要中心点：重心、外心、垂心、内心和九点圆心。②涉及的核心数学概念包括：重心、外心、垂心、内心、九点圆、欧拉线、向量、解析几何。③作图要点：使用Polygon命令构造三角形，用Circle命令画外接圆和九点圆，通过Intersect命令求交点，用Midpoint命令找中点，Line命令画直线，OrthogonalLine命令画垂线，Segment命令画线段。④适合高中及以上学生学习和理解三角形几何性质，也可用于竞赛数学和几何作图教学。

GeoGebra 命令及参数

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Circle(C, D) → d
  3. Circle(B, E) → e
  4. Circle(A, F) → f
  5. Intersect(d, b, 1) → G
  6. Intersect(d, a, 1) → H
  7. Intersect(e, a, 1) → I
  8. Intersect(e, c, 1) → J
  9. Intersect(f, c, 1) → K
  10. Intersect(f, b, 1) → L
  11. Midpoint(L, K) → M
  12. Midpoint(J, I) → N
  13. Midpoint(H, G) → O
  14. Line(C, O) → g
  15. Line(B, N) → h
  16. Line(A, M) → i
  17. Intersect(g, h) → lncenter
  18. Intersect(g, i) → Incenter_.
  19. Intersect(h, i) → Incenter
  20. OrthogonalLine(Incenter, c) → j
  21. OrthogonalLine(Incenter, a) → k
  22. OrthogonalLine(Incenter, b) → l
  23. Intersect(j, c) → S
  24. Circle(Incenter, S) → p
  25. OrthogonalLine(Incenter_., c) → m
  26. OrthogonalLine(Incenter_., a) → n
  27. OrthogonalLine(Incenter_., b) → q
  28. Intersect(m, c) → T
  29. Circle(Incenter_., T) → r
  30. OrthogonalLine(lncenter, c) → s
  31. OrthogonalLine(lncenter, b) → t
  32. OrthogonalLine(lncenter, a) → f_1
  33. Intersect(s, c) → U
  34. Circle(lncenter, U) → c_1
  35. Midpoint(b) → Pm_3
  36. Midpoint(a) → Pm_2
  37. Midpoint(c) → Pm_1
  38. Line(C, Pm_1) → g_1
  39. Line(Pm_2, A) → h_1
  40. Line(Pm_3, B) → i_1
  41. Intersect(g_1, h_1) → Centroid
  42. OrthogonalLine(C, c) → j_1
  43. OrthogonalLine(A, a) → k_1
  44. OrthogonalLine(B, b) → l_1
  45. Intersect(j_1, k_1) → Orthocenter
  46. Intersect(l_1, b) → Ph_3
  47. Intersect(j_1, c) → Ph_1
  48. Intersect(k_1, a) → Ph_2
  49. Segment(Orthocenter, C) → m_1
  50. Segment(Orthocenter, B) → n_1
  51. Segment(Orthocenter, A) → p_1
  52. Midpoint(n_1) → P_H2
  53. Midpoint(p_1) → P_H1
  54. Midpoint(m_1) → P_H3
  55. OrthogonalLine(Pm_2, a) → q_1
  56. OrthogonalLine(Pm_1, c) → r_1
  57. OrthogonalLine(Pm_3, b) → s_1
  58. Intersect(q_1, r_1) → Circumcenter
  59. Circle(Circumcenter, A) → Cirumcircle
  60. Midpoint(Orthocenter, Circumcenter) → NinePointCenter
  61. Circle(NinePointCenter, Pm_1) → NinePointCircle
  62. Line(Circumcenter, Orthocenter) → t_1
  63. Line(Circumcenter, Orthocenter) → TheEulerLine