同圆心的内切圆

同圆心的内切圆
几何画板及绘图内容加载中,请稍等……
2017-08-16 05:23
当另一个圆与任意三角形的内切圆具有相同的圆心时,会发生什么?通过互动工作表探索这一现象。本范例涉及三角形的内切圆及其性质。使用GeoGebra命令如Line, Rotate, Angle, Circle等进行几何作图。适合初中及以上学生学习三角函数和几何作图。

GeoGebra 命令及参数

  1. Line(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Line(A, C) → i
  8. Line(C, B) → j
  9. Segment(A, B) → k
  10. Segment(A, C) → l
  11. Min({h, k, l}) → b
  12. Angle(C, B, A) → β
  13. Rotate(B, α / 2, A) → B'_1
  14. Angle(B, A, B'_1) → γ
  15. Rotate(C, β / 2, B) → C'
  16. Angle(C, B, C') → δ
  17. Ray(A, B'_1) → m
  18. Ray(B, C') → n
  19. Intersect(m, n) → D
  20. Segment(D, C) → p
  21. Segment(D, A) → q
  22. Segment(D, B) → r
  23. Max({p, q, r}) → c
  24. Circle(D, d) → e
  25. Intersect(e, j, 1) → E
  26. Intersect(e, i, 2) → F
  27. Intersect(e, j, 2) → G
  28. Intersect(e, f) → H, I
  29. Intersect(e, i, 1) → J
  30. Segment(A, D) → s
  31. Segment(B, D) → t
  32. Min({s, t}) → o
  33. Segment(A, B) → f_1
  34. Circle(A, (0.35 * o)) → c_1
  35. Circle(B, (0.35 * o)) → d_1
  36. Intersect(c_1, f_1, 1) → K
  37. Intersect(c_1, s, 1) → L
  38. Intersect(d_1, h) → M,
  39. Intersect(d_1, t, 1) → N
  40. Polygon(H, A, J) → poly1, j_1, h_1, a_1
  41. Polygon(B, I, G) → poly2, g_1, b_1, i_1
  42. Polygon(C, F, E) → poly3, e_1, c_2, f_2
  43. Polygon(A, B, C) → poly4, c_3, a_2, b_2
  44. Angle(A, C, B) → ε
  45. CircleSector(B, M, N) → k_1
  46. CircleSector(A, K, L) → p_1
  47. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'
  48. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], D) → B'_2
  49. Segment(B, B'_2) → l_1
  50. Segment(A, A') → m_1
  51. Rotate(p_1, If[2 < u ≤ 3, ((u - 2) * γ), γ], A) → q_1
  52. Rotate(k_1, If[3 < u ≤ 4, ((u - 3) * δ), δ], B) → r_1
  53. Dilate(D, If[4 < u ≤ 5, 5 - u, 0], F) → D'
  54. Circle(D, D') → s_1
  55. Segment(D, D') → n_1
  56. Dilate(C, If[5 < u ≤ 6, 6 - u, 0], F) → C'_1
  57. Dilate(C, If[5 < u ≤ 6, 6 - u, 0], E) → C'_2
  58. Dilate(A, If[5 < u ≤ 6, 6 - u, 0], H) → A'_1
  59. Dilate(A, If[5 < u ≤ 6, 6 - u, 0], J) → A'_2
  60. Dilate(B, If[5 < u ≤ 6, 6 - u, 0], I) → B'_3
  61. Dilate(B, If[5 < u ≤ 6, 6 - u, 0], G) → B'_4
  62. Segment(C, C'_1) → t_1
  63. Segment(C, C'_2) → g_2
  64. Segment(A, A'_1) → h_2
  65. Segment(A, A'_2) → i_2
  66. Segment(B, B'_3) → j_2
  67. Segment(B, B'_4) → k_2
  68. Dilate(F, If[6 < u ≤ 7, 7 - u, 0], E) → F'
  69. Dilate(H, If[6 < u ≤ 7, 7 - u, 0], J) → H'
  70. Dilate(G, If[6 < u ≤ 7, 7 - u, 0], I) → G'
  71. Segment(F, F') → l_2
  72. Segment(H, H') → m_2
  73. Segment(G, G') → n_2
  74. Rotate(C, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → C'_3
  75. Rotate(C'_1, If[7 < u ≤ 8, ((u - 7) * ε), ε], C) → O
  76. Segment(C'_3, O) → p_2
  77. Rotate(A, If[8 < u ≤ 9, ((u - 8) * α), α], A) → A'_3
  78. Rotate(A'_1, If[8 < u ≤ 9, ((u - 8) * α), α], A) → P
  79. Segment(A'_3, P) → q_2
  80. Rotate(B, If[9 < u ≤ 10, ((u - 9) * β), β], B) → B'_5
  81. Rotate(B'_4, If[9 < u ≤ 10, ((u - 9) * β), β], B) → Q
  82. Segment(B'_5, Q) → r_2

AI 绘图提示语参考

绘制一个三角形ABC,然后以三角形ABC的内心为中心画一个圆。接着,通过旋转和角度计算,构造出与内心圆同心的另一个圆,并找到该圆与三角形边的交点,形成新的三角形DEF。最后,通过缩放操作,调整三角形ABC的顶点位置,观察变化。
以上提示语为根据原始绘图命令整理而来,仅供参考。