三角形特殊线段与外接圆动态演示

三角形特殊线段与外接圆动态演示
几何画板及绘图内容加载中,请稍等……
2017-10-11 08:46
①本范例动态演示三角形内角平分线、中线、高线与外接圆的关系;②涉及核心概念:外接圆、三角形特殊线段、角度、几何变换;③构造要点:运用 Rotate, Ray, Point, Segment, Line, Intersect, Angle, Polygon, Circle, LineBisector, Min, Dilate, CircleSector, Vector, Translate 等命令构建图形;④适合高中及以上数学教学,用于理解几何性质与动态变化。

GeoGebra 命令及参数

  1. Rotate(C, (a * π / 180), A) → A'
  2. Ray(A, A') → g
  3. Point(g) → B
  4. Segment(B, C) → h
  5. Segment(A, B) → i
  6. Point(i) → D
  7. Segment(A, C) → f
  8. Line(D, f) → j
  9. Intersect(j, h) → E
  10. Segment(E, C) → m
  11. Line(B, A) → k
  12. Point(h) → F
  13. Angle(C, A, A') → α
  14. Polygon(A, C, B) → t1, c_1, b, a_1
  15. Polygon(D, E, F) → t2, f_1, d_1, e
  16. Segment(D, F) → l
  17. Circle(B, 2) → p
  18. Circle(A, 2) → q
  19. Intersect(p, k, 1) → H
  20. Intersect(q, k, 2) → I
  21. Ray(B, H) → n
  22. Ray(A, I) → r
  23. LineBisector(E, F) → s
  24. LineBisector(E, D) → t
  25. Segment(D, B) → g_1
  26. Segment(D, A) → h_1
  27. Min(g_1, h_1) → o
  28. Circle(A, (0.3 * o)) → e_1
  29. Circle(D, (0.3 * o)) → k_1
  30. Intersect(e_1, k) → K, L
  31. LineBisector(C, F) → j_1
  32. Dilate(D, If[0 < u ≤ 1, 1 - u, 0], E) → D'
  33. Segment(D, D') → l_1
  34. Rotate(K, If[1 < u ≤ 2, ((-(u - 1)) * α), (-α)], A) → K'
  35. CircleSector(A, K', K) → p_1
  36. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], D) → B'
  37. Vector(A, B') → v
  38. Translate(p_1, v) → q_1
  39. Dilate(D, If[4 < u ≤ 5, 5 - u, 0], F) → D'_1
  40. Segment(D, D'_1) → m_1
  41. Ray(D, A) → n_1
  42. LineBisector(E, F) → c
  43. LineBisector(F, D) → d
  44. LineBisector(F, C) → t_1
  45. LineBisector(D, E) → i_1
  46. LineBisector(F, D) → r_1
  47. Intersect(r_1, i_1) → G_1
  48. Circle(G_1, F) → s_1
  49. LineBisector(F, C) → f_2
  50. Intersect(s_1, k) → G, J
  51. LineBisector(J, A) → b_1
  52. LineBisector(C, F) → g_2
  53. Intersect(g_2, b_1) → M
  54. Circle(M, C) → c_2
  55. Ray(D, B) → h_2
  56. Intersect(s_1, h_2) → N, O
  57. LineBisector(O, A) → i_2
  58. LineBisector(C, F) → j_2
  59. Intersect(i_2, j_2) → P
  60. Circle(P, C) → d_2
  61. Dilate(G_1, If[6 < u ≤ 7, 7 - u, 0], F) → Q
  62. Segment(G_1, Q) → k_2
  63. Circle(G_1, Q) → e_2
  64. Dilate(P, If[8.5 < u ≤ 9.5, 9.5 - u, 0], C) → P'
  65. Segment(P, P') → l_2
  66. Circle(P, P') → p_2
  67. Dilate(M, If[8.5 < u ≤ 9.5, 9.5 - u, 0], C) → M'
  68. Segment(M, M') → m_2
  69. Circle(M, M') → q_2

AI 绘图提示语参考

画一个三角形,并动态展示其角平分线、中线、高线与外接圆的关系。首先绘制三角形,然后找到各边的中点和高线交点,绘制角平分线、中线和高线。接着,以三角形的顶点为圆心绘制外接圆,并找到角平分线与外接圆的交点。最后,通过旋转和缩放操作,动态展示这些几何元素之间的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。