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动画演示直角三角形与内切圆关系

动画演示直角三角形与内切圆关系
几何画板及绘图内容加载中，请稍等……
2017-05-26 22:15
测试改名0圆几何作图
①本范例通过动画演示直角三角形内切圆的动态变化与性质；②涉及核心数学概念包括内切圆、直角三角形、二次方程、函数、几何变换等；③构造过程中运用了Ray, Point, Segment, Line, Circle, Rotate, Dilate等GeoGebra命令；④适合高中数学教学，用于理解几何变换与函数图像的关联。

GeoGebra 命令及参数

  1. Ray(A, B) → g
  2. Point(g) → F
  3. Ray(A, F) → h
  4. Point(h) → G
  5. Segment(A, G) → k
  6. Line(A, B) → a
  7. OrthogonalLine(A, a) → d
  8. Point(d) → E
  9. Ray(A, E) → i
  10. Point(i) → H
  11. Line(A, H) → m
  12. Segment(A, H) → j
  13. Circle(A, Min[(0.15 * j), (0.15 * k)]) → p
  14. Intersect(p, m) → O, P
  15. Intersect(p, a) → M, N
  16. OrthogonalLine(B, a) → e
  17. Point(d) → C
  18. Ray(A, C) → c
  19. Ray(A, E) → b
  20. Intersect(p, a, 2) → I
  21. Intersect(p, i, 1) → J
  22. Intersect(p, a, 1) → K
  23. Polygon(A, G, H) → poly1, h_1, a_1, g_1
  24. CircleSector(A, N, P) → q
  25. Rotate(q, If[0 < f ≤ 1, (f * π / 2), π / 2], A) → q'
  26. Rotate(G, 45°, A) → G'
  27. Angle(G, A, G') → α
  28. Angle(H, G, A) → β
  29. Rotate(H, β / 2, G) → H'
  30. Angle(H, G, H') → γ
  31. Ray(G, H') → l
  32. Ray(A, G') → n
  33. Intersect(l, n) → D
  34. Line(H, G) → r
  35. Intersect(r, n) → L
  36. Intersect(l, m) → Q
  37. Dilate(A, If[1 < f ≤ 2, 2 - f, 0], L) → A'
  38. Segment(A, A') → s
  39. Intersect(p, n) → R,
  40. Circle(G, (0.15 * Distance[A, G])) → t
  41. Intersect(t, r) → S, T
  42. Intersect(t, l) → U,
  43. CircleSector(G, S, U) → d_1
  44. CircleSector(A, R, P) → c_1
  45. Dilate(G, If[2 < f ≤ 3, 3 - f, 0], D) → G'_1
  46. Segment(G, G'_1) → f_1
  47. Rotate(c_1, If[3 < f ≤ 4, ((-(f - 3)) * π / 4), ((-π)) / 4], A) → e_1
  48. Rotate(d_1, If[4 < f ≤ 5, ((f - 4) * γ), γ], G) → k_1
  49. OrthogonalLine(D, a) → i_1
  50. Intersect(a, i_1) → V
  51. OrthogonalLine(D, r) → j_1
  52. OrthogonalLine(D, m) → l_1
  53. Intersect(j_1, r) → W
  54. Intersect(l_1, m) → Z
  55. Angle(G, V, D) → δ
  56. Dilate(D, If[5 < f ≤ 6, 6 - f, 0], V) → D'
  57. Segment(D, D') → m_1
  58. Angle(V, D, W) → ε
  59. Angle(W, D, Z) → ζ
  60. Angle(Z, D, V) → η
  61. Rotate(V, If[6 < f ≤ 7, ((f - 6) * ε), ε], D) → V'
  62. CircleArc(D, V, V') → p_1
  63. Rotate(W, If[7 < f ≤ 8, ((f - 7) * ζ), ζ], D) → W'
  64. CircleArc(D, W, W') → q_1
  65. Rotate(Z, If[8 < f ≤ 9, ((f - 8) * π / 2), π / 2], D) → Z'
  66. CircleArc(D, Z, Z') → r_1
  67. Circle(D, V) → s_1
  68. Line(Z, W) → n_1
  69. Intersect(l, n_1) → A_1
  70. Dilate(Z, If[9 < f ≤ 10, 10 - f, 0], W) → Z'_1
  71. Segment(Z, Z'_1) → t_1
  72. Dilate(D, If[10 < f ≤ 11, 11 - f, 0], A_1) → D'_1
  73. Segment(D, D'_1) → b_1
  74. Line(A, f_1) → f_2
  75. Point(f_2) → B_1
  76. Angle(B_1, A, G) → θ
  77. Dilate(A, If[11 < f ≤ 12, 12 - f, 0], A_1) → A'_1
  78. Vector(A, A'_1) → u
  79. Translate(e_1, u) → c_2
  80. Rotate(c_2, If[12 < f ≤ 13, ((-(f - 12)) * θ), (-θ)], A_1) → d_2
  81. Segment(A, H) → g_2
  82. Segment(H, G) → h_2