积极 AI Logo 积极 AI

三角形高线与外接圆动态关系

三角形高线与外接圆动态关系
几何画板及绘图内容加载中，请稍等……
2017-05-23 08:49
测试改名0圆几何作图轨迹
①本范例演示了三角形两条高线、外接圆以及从第三顶点引出的切线之间的动态可变关系；②涉及核心数学概念包括外接圆、乘积、除法、高线、切线、旋转、向量等；③作图要点提炼自GeoGebra命令：Rotate（旋转）、Ray（射线）、Point（点）、Segment（线段）、Line（直线）、OrthogonalLine（垂线）、Intersect（交点）、Min（最小值）、Circle（圆）、Angle（角度）、LineBisector（角平分线）、CircleArc（圆弧）、Dilate（缩放）、CircleSector（扇形）、Vector（向量）、Translate（平移）、Polygon（多边形）；④适合高中及以上数学学习者探索几何关系与动态几何软件应用。

GeoGebra 命令及参数

  1. Rotate(B, (a * π / 180), A) → B'
  2. Ray(A, B') → g
  3. Point(g) → C
  4. Segment(A, C) → q_1
  5. Line(C, B) → r
  6. Line(A, C) → q
  7. OrthogonalLine(B, q) → f_1
  8. Intersect(q, f_1) → H
  9. Segment(C, H) → r_1
  10. Min(q_1, r_1) → v
  11. Circle(C, (0.4 * v)) → s_1
  12. Intersect(s_1, r) → O, P
  13. Intersect(s_1, q) → M, N
  14. Angle(M, C, P) → ζ
  15. Segment(C, B) → j
  16. LineBisector(j) → k
  17. Segment(A, C) → i
  18. LineBisector(i) → l
  19. Intersect(k, l) → D
  20. Line(D, C) → m
  21. OrthogonalLine(C, m) → n
  22. Intersect(s_1, n) → Q, R
  23. Angle(A, C, Q) → κ
  24. Angle(B, A, B') → α
  25. Ray(A, B) → f
  26. Segment(A, B) → h
  27. Rotate(C, If[0 < b ≤ 2, ((b - 2) * π), (2 * π)], D) → C'
  28. CircleArc(D, C, C') → c
  29. Circle(D, C) → d
  30. Circle(C, 3) → e
  31. Intersect(e, n, 1) → E
  32. Intersect(e, n, 2) → F
  33. Angle(D, C, E) → β
  34. Dilate(D, If[2 < b ≤ 3, 3 - b, 0], C) → D'
  35. Segment(D, D') → p
  36. OrthogonalLine(A, r) → s
  37. Intersect(r, s) → G
  38. Angle(A, G, B) → γ
  39. Dilate(A, If[3 < b ≤ 4, 4 - b, 0], G) → A'
  40. Segment(A, A') → t
  41. Dilate(B, If[4 < b ≤ 5, 5 - b, 0], H) → B'_1
  42. Segment(B, B'_1) → g_1
  43. Angle(A, H, B) → δ
  44. Dilate(H, If[5 < b ≤ 6, 6 - b, 0], G) → H'
  45. Segment(H, H') → h_1
  46. Line(H, G) → i_1
  47. Segment(H, C) → j_1
  48. Segment(H, A) → k_1
  49. Intersect(d, i_1) → I, J
  50. Segment(H, G) → l_1
  51. Segment(H, I) → m_1
  52. Min({j_1, k_1, l_1, m_1}) → o
  53. Circle(H, (0.4 * o)) → c_1
  54. Intersect(c_1, q, 1) → K
  55. Intersect(c_1, i_1, 2) → L
  56. Angle(K, H, L) → ε
  57. Rotate(K, If[7 < b ≤ 8, ((b - 7) * ε), ε], H) → K'
  58. CircleSector(H, K, K') → d_1
  59. Dilate(H, If[8.5 < b ≤ 9.5, 9.5 - b, 0], C) → H'_1
  60. Vector(H, H'_1) → u
  61. Translate(d_1, u) → e_1
  62. Polygon(A, B, C) → poly1, c_2, a_1, b_1
  63. Segment(A, B) → n_1
  64. Segment(A, H) → p_1
  65. Rotate(M, If[7 < b ≤ 8, ((b - 7) * κ), κ], C) → M'
  66. CircleSector(C, M, M') → t_1
  67. Dilate(C, If[8.5 < b ≤ 9.5, 9.5 - b, 0], H) → C'_1
  68. Vector(C, C'_1) → w
  69. Translate(t_1, w) → d_2
  70. Dilate(D, If[-1 < b < 0, (-b), 0], C) → D'_1
  71. Segment(D, D'_1) → f_2
  72. Rotate(D, If[0 < b ≤ 2, ((b - 2) * π), (2 * π)], D) → D'_2
  73. Rotate(D'_1, If[0 < b ≤ 2, ((b - 2) * π), (2 * π)], D) → T
  74. Segment(D'_2, T) → g_2
  75. Segment(C, A) → h_2
  76. Min(h_2, n_1) → o_1
  77. Circle(A, (0.15 * o_1)) → e_2
  78. Intersect(e_2, n_1) → U,
  79. Intersect(e_2, h_2) → V,
  80. CircleSector(A, U, V) → k_2