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费尔巴赫定理与费尔巴赫点

费尔巴赫定理与费尔巴赫点
几何画板及绘图内容加载中，请稍等……
2015-02-14 06:03
测试改名0圆几何作图
所属专题 A Tour of Triangle Geometry
该范例演示了费尔巴赫定理，即九点圆内切于内切圆且外切于三个旁切圆。通过使用GeoGebra命令如Line, OrthogonalLine, LineBisector等，可以构造出九点圆、内切圆和旁切圆，并观察它们之间的关系。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. Line(A, B) → m
  2. Line(C, A) → n
  3. Line(B, C) → q
  4. OrthogonalLine(A, q) → a
  5. OrthogonalLine(B, n) → b
  6. OrthogonalLine(C, m) → c
  7. LineBisector(B, C) → d
  8. LineBisector(C, A) → e
  9. LineBisector(A, B) → f
  10. Intersect(q, a) → D
  11. Intersect(n, e) → E
  12. Intersect(n, b) → F_1
  13. Intersect(m, c) → G_1
  14. Intersect(m, f) → I
  15. Intersect(q, d) → J
  16. Circle(G_1, D, E) → k
  17. Segment(A, J) → i
  18. Segment(B, E) → j
  19. Segment(I, C) → l
  20. Intersect(i, j) → G
  21. AngularBisector(n, m) → g, h
  22. AngularBisector(q, m) → p, r
  23. AngularBisector(n, q) → s, t
  24. Intersect(g, p) → H
  25. Intersect(h, r) → K
  26. Intersect(h, p) → L
  27. Intersect(g, r) → M
  28. OrthogonalLine(M, q) → a_1
  29. OrthogonalLine(L, q) → b_1
  30. OrthogonalLine(H, n) → c_1
  31. Intersect(n, c_1) → N
  32. Circle(H, N) → d_1
  33. Intersect(q, a_1) → O
  34. Circle(M, O) → e_1
  35. Intersect(q, b_1) → P
  36. Circle(L, P) → f_1
  37. OrthogonalLine(K, q) → g_1
  38. Intersect(q, g_1) → Q
  39. Circle(K, Q) → h_1
  40. Intersect(h_1, k) → F, , ,