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九点圆的探索

九点圆的探索
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2015-08-16 11:19
测试改名0圆几何作图
所属专题 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry Review Triangle Theorems Triangles: Points of Concurrency
①本范例通过可视化方式演示任意三角形的九点圆及其性质；②涉及核心数学概念包括三角形、圆、中点、垂足、外心、重心、垂心等；③作图要点：使用Segment（线段）、Midpoint（中点）、OrthogonalLine（垂线）、Intersect（交点）、Circle（圆）、Center（圆心）等GeoGebra命令；④适合高中数学教学，用于探究九点圆定理及相关性质。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. Midpoint(c) → E_1
  5. Midpoint(b) → F_1
  6. Midpoint(a) → G_1
  7. OrthogonalLine(C, a) → l
  8. OrthogonalLine(A, b) → m
  9. OrthogonalLine(B, c) → n
  10. Intersect(l, m) → I_1
  11. Intersect(l, a) → G
  12. Intersect(n, c) → I
  13. Intersect(m, b) → H
  14. Midpoint(a) → D
  15. Midpoint(c) → F
  16. Midpoint(b) → E
  17. Midpoint(I_1, A) → L
  18. Midpoint(I_1, B) → J
  19. Midpoint(I_1, C) → K
  20. Circle(D, J, E) → d
  21. Center(d) → R
  22. Angle(a, l) → α
  23. Angle(b, m) → β
  24. Angle(c, n) → γ
  25. Segment(A, L) → e
  26. Segment(L, I_1) → f
  27. Segment(C, K) → g
  28. Segment(K, I_1) → h
  29. Segment(B, J) → i
  30. Segment(J, I_1) → j
  31. Line(B, I) → k
  32. LineBisector(c) → q
  33. LineBisector(b) → r
  34. LineBisector(a) → p
  35. Intersect(q, r) → M
  36. Angle(c, q) → δ
  37. Angle(a, p) → ε
  38. Angle(b, r) → ζ
  39. Segment(C, D) → s
  40. Segment(B, F) → t
  41. Intersect(s, t) → N
  42. Segment(A, E) → a_1
  43. AngularBisector(c, a) → b_1, c_1
  44. AngularBisector(c, b) → d_1, e_1
  45. AngularBisector(b, a) → f_1, g_1
  46. Intersect(c_1, e_1) → O
  47. OrthogonalLine(O, a) → h_1
  48. Intersect(h_1, a) → P
  49. Circle(O, P) → k_1