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三角形内切圆与边中点关系动态演示

三角形内切圆与边中点关系动态演示
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2017-06-21 10:12
测试改名0圆几何作图滑块动画轨迹
①本范例动态演示三角形内切圆与其两边中点构成的几何关系；②涉及核心概念：内切圆、相似三角形、几何变换；③作图要点：运用了中点、线段、缩放、旋转、多边形、角度、射线、交点、垂线、最小值、圆、圆扇形、圆弧、直线等GeoGebra命令与对象；④适合高中数学教学或几何爱好者探索。

GeoGebra 命令及参数

  1. Midpoint(A, B) → D
  2. Midpoint(B, C) → E
  3. Midpoint(C, A) → F
  4. Segment(A, B) → a
  5. Segment(B, C) → b
  6. Segment(C, A) → c
  7. Segment(C, D) → d
  8. Segment(A, E) → e
  9. Segment(B, F) → f
  10. Dilate(A, If[0 < g ≤ 1, 1 - g, 0], D) → A'
  11. Segment(A, A') → h
  12. Rotate(A, If[1 < g ≤ 2, ((-(g - 1)) * π), (-π)], D) → A'_1
  13. Rotate(A', If[1 < g ≤ 2, ((g - 1) * π), 3.141592653589793], D) → A''
  14. Segment(A'_1, A'') → h'
  15. Dilate(B, If[2 < g ≤ 3, 3 - g, 0], E) → B'
  16. Segment(B, B') → i
  17. Rotate(B, If[3 < g ≤ 4, ((-(g - 3)) * π), (-π)], E) → B'_1
  18. Rotate(B', If[3 < g ≤ 4, ((g - 3) * π), 3.141592653589793], E) → B''
  19. Segment(B'_1, B'') → i'
  20. Dilate(C, If[4 < g ≤ 5, 5 - g, 0], F) → C'
  21. Segment(C, C') → j
  22. Rotate(C, If[5 < g ≤ 6, ((-(g - 5)) * π), (-π)], F) → C'_1
  23. Rotate(C', If[5 < g ≤ 6, ((g - 5) * π), 3.141592653589793], F) → C''
  24. Segment(C'_1, C'') → j'
  25. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  26. Angle(B, A, C) → α
  27. Angle(A, C, B) → β
  28. Angle(C, B, A) → γ
  29. Rotate(B, α / 2, A) → B'_2
  30. Angle(B, A, B'_2) → δ
  31. Ray(A, B'_2) → k
  32. Rotate(C, γ / 2, B) → C'_3
  33. Angle(C, B, C'_3) → ε
  34. Ray(B, C'_3) → l
  35. Intersect(k, l) → O
  36. Segment(C, B) → m
  37. Segment(C, A) → n
  38. Intersect(m, k) → P
  39. Intersect(l, n) → Q
  40. Segment(A, B) → s
  41. OrthogonalLine(O, s) → t
  42. OrthogonalLine(O, m) → f_1
  43. Segment(C, A) → g_1
  44. OrthogonalLine(O, g_1) → h_1
  45. Intersect(h_1, g_1) → R
  46. Intersect(t, s) → S
  47. Intersect(f_1, m) → T
  48. Dilate(O, If[10 < g ≤ 11, 11 - g, 0], S) → O'
  49. Segment(O, O') → i_1
  50. Min({g_1, s, m}) → o
  51. Circle(A, (0.25 * o)) → d_1
  52. Circle(B, (0.25 * o)) → e_1
  53. Intersect(d_1, g_1) → U,
  54. Intersect(d_1, s) → V,
  55. Intersect(e_1, m) → W,
  56. Intersect(e_1, s) → Z,
  57. Intersect(d_1, k) → A_1,
  58. Intersect(e_1, l) → B_1,
  59. CircleSector(A, V, A_1) → k_1
  60. CircleSector(B, W, B_1) → p_1
  61. Dilate(A, If[6 < g ≤ 7, 7 - g, 0], O) → A'_3
  62. Segment(A, A'_3) → j_1
  63. Dilate(B, If[7 < g ≤ 8, 8 - g, 0], O) → B'_3
  64. Segment(B, B'_3) → p
  65. Rotate(k_1, If[8 < g ≤ 9, ((g - 8) * δ), δ], A) → q
  66. Rotate(p_1, If[9 < g ≤ 10, ((g - 9) * ε), ε], B) → r
  67. Angle(O, S, A) → ζ
  68. Rotate(S, If[11 < g ≤ 13, ((g - 11) * π), (2 * π)], O) → S'
  69. CircleArc(O, S, S') → q_1
  70. Circle(O, S) → r_1
  71. Segment(F, E) → l_1
  72. Line(C, S) → m_1
  73. Intersect(m_1, l_1) → G
  74. Dilate(C, If[13 < g ≤ 14, 14 - g, 0], S) → C'_2
  75. Segment(C, C'_2) → n_1
  76. Dilate(E, If[14 < g ≤ 15, 15 - g, 0], G) → E'
  77. Segment(E, E') → s_1
  78. Dilate(G, If[15 < g ≤ 16, 16 - g, 0], F) → G'
  79. Segment(G, G') → t_1
  80. Dilate(D, If[16 < g ≤ 17, 17 - g, 0], O) → D'
  81. Segment(D, D') → f_2
  82. Dilate(O, If[17 < g ≤ 18, 18 - g, 0], G) → O'_1
  83. Segment(O, O'_1) → g_2