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等腰直角三角形外接圆与斜边切线动态演示

等腰直角三角形外接圆与斜边切线动态演示
几何画板及绘图内容加载中，请稍等……
2017-07-04 11:20
测试改名0圆几何作图
①本范例动态演示等腰直角三角形的外接圆与斜边相切的关系；②涉及核心数学概念包括圆、等腰三角形、切线、三角函数、几何作图；③构造要点：运用了Circle（圆）、Segment（线段）、OrthogonalLine（垂线）、Rotate（旋转）、Angle（角度）、Ray（射线）、Intersect（交点）、Polygon（多边形）、Line（直线）、Point（点）、Dilate（缩放）、CircleSector（扇形）、Vector（向量）、CircleArc（圆弧）、Midpoint（中点）、Translate（平移）等GeoGebra命令/对象；④适合高中数学教学，用于理解圆与三角形、切线性质及动态几何关系。

GeoGebra 命令及参数

  1. Circle(B, C) → c
  2. Segment(B, C) → a
  3. OrthogonalLine(C, a) → b
  4. Rotate(C, 45°, B) → C'
  5. Angle(C, B, C') → α
  6. Ray(B, C') → d
  7. Intersect(b, d) → A
  8. Segment(A, C) → e
  9. Segment(B, A) → f
  10. Polygon(B, C, A) → poly1, a_1, b_1, c_1
  11. Line(B, C) → h
  12. Point(h) → D
  13. Point(h) → E
  14. Ray(C, E) → i
  15. Point(i) → F
  16. Ray(C, F) → j
  17. Dilate(B, If[0 < g ≤ 1, 1 - g, 0], C) → B'
  18. Segment(B, B') → k
  19. Dilate(C, If[1 < g ≤ 2, 2 - g, 0], A) → C'_1
  20. Segment(C, C'_1) → l
  21. Circle(C, (0.15 * a)) → p
  22. Intersect(p, j, 1) → G
  23. Intersect(p, e, 1) → H
  24. Intersect(p, a, 1) → I
  25. Circle(A, (0.15 * a)) → q
  26. Circle(B, (0.15 * a)) → r
  27. Intersect(q, e, 1) → J
  28. Intersect(q, f, 1) → K
  29. CircleSector(C, H, I) → s
  30. Dilate(A, If[2 < g ≤ 3, 3 - g, 0], B) → A'
  31. Segment(A, A') → m
  32. Rotate(s, If[3.5 < g ≤ 4.5, ((-(g - 3.5)) * π / 2), -1.5707963267948966], C) → s'
  33. Dilate(A, If[5.5 < g ≤ 6.5, 6.5 - g, 0], B) → A'_1
  34. Vector(A, A'_1) → u
  35. Rotate(B, If[4.5 < g ≤ 5.5, ((-(g - 4.5)) * π / 2), -1.5707963267948966], C) → B'_1
  36. Rotate(B', If[4.5 < g ≤ 5.5, ((-(g - 4.5)) * π / 2), -1.5707963267948966], C) → B''
  37. Segment(B'_1, B'') → k'
  38. Dilate(A, If[7.5 < g ≤ 8.5, 8.5 - g, 0], C) → A'_2
  39. Vector(A, A'_2) → v
  40. Dilate(A, If[9.5 < g ≤ 10.5, 10.5 - g, 0], C) → A'_3
  41. Vector(A, A'_3) → w
  42. Line(B, C) → n
  43. Circle(B, 1) → t
  44. Line(C, A) → f_1
  45. Circle(A, 1) → d_1
  46. Intersect(d_1, f_1, 2) → L
  47. Intersect(t, n, 1) → M
  48. Ray(A, L) → g_1
  49. Ray(B, M) → h_1
  50. Rotate(L, 67.5°, A) → L'
  51. Angle(L, A, L') → β
  52. Rotate(A, 67.5°, B) → A'_4
  53. Angle(A, B, A'_4) → γ
  54. Ray(A, L') → i_1
  55. Ray(B, A'_4) → j_1
  56. Circle(B, (0.25 * k)) → e_1
  57. Circle(A, (0.25 * k)) → k_1
  58. Intersect(e_1, h_1, 1) → N
  59. Intersect(e_1, j_1) → O,
  60. Intersect(k_1, i_1) → P,
  61. Intersect(k_1, g_1) → Q,
  62. CircleSector(A, Q, P) → p_1
  63. CircleSector(B, O, N) → q_1
  64. Intersect(i_1, j_1) → R
  65. OrthogonalLine(R, h_1) → l_1
  66. OrthogonalLine(R, g_1) → m_1
  67. Intersect(m_1, g_1) → S
  68. Intersect(h_1, l_1) → T
  69. Angle(B, T, R) → δ
  70. Angle(R, S, A) → ε
  71. Dilate(A, If[5.5 < g ≤ 6.5, 6.5 - g, 0], R) → A'_5
  72. Dilate(B, If[5.5 < g ≤ 6.5, 6.5 - g, 0], R) → B'_2
  73. Segment(A, A'_5) → n_1
  74. Segment(B, B'_2) → r_1
  75. Dilate(R, If[6.5 < g ≤ 7.5, 7.5 - g, 0], T) → R'
  76. Dilate(R, If[6.5 < g ≤ 7.5, 7.5 - g, 0], S) → R'_1
  77. Segment(R, R') → s_1
  78. Segment(R, R'_1) → t_1
  79. Rotate(T, If[8.5 < g ≤ 10.5, ((g - 8.5) * π), (2 * π)], R) → T'
  80. Rotate(p_1, If[7.5 < g ≤ 8.5, (((g - 7.5) * 67.5) * π / 180), (67.5 * π / 180)], A) → c_2
  81. Rotate(q_1, If[7.5 < g ≤ 8.5, (((-(g - 7.5)) * 67.5) * π / 180), (-67.5 * π / 180)], B) → d_2
  82. CircleArc(R, T, T') → e_2
  83. Circle(R, T) → f_2
  84. Line(R, A) → g_2
  85. OrthogonalLine(C, g_2) → h_2
  86. Intersect(g_2, h_2) → V
  87. Angle(A, V, C) → ζ
  88. Dilate(C, If[10.5 < g ≤ 11.5, 11.5 - g, 0], V) → C'_2
  89. Dilate(A, If[10.5 < g ≤ 11.5, 11.5 - g, 0], V) → A'_6
  90. Segment(A, A'_6) → i_2
  91. Segment(C, C'_2) → j_2
  92. Midpoint(R, A) → U
  93. Dilate(A, If[11.5 < g ≤ 12.5, 12.5 - g, 0], U) → A'_7
  94. Segment(A, A'_7) → k_2
  95. Dilate(U, If[12.5 < g ≤ 13.5, 13.5 - g, 0], R) → U'
  96. Segment(U, U') → l_2
  97. Dilate(V, If[13.5 < g ≤ 14.5, 14.5 - g, 0], A) → V'
  98. Vector(V, V') → u_1
  99. Translate(C, u_1) → C'_3
  100. Translate(C'_2, u_1) → W
  101. Segment(C'_3, W) → m_2
  102. Rotate(C'_3, If[14.5 < g ≤ 15.5, ((-(g - 14.5)) * π / 2), ((-π)) / 2], A) → Z
  103. Rotate(W, If[14.5 < g ≤ 15.5, ((-(g - 14.5)) * π / 2), ((-π)) / 2], A) → W'
  104. Segment(Z, W') → n_2
  105. Rotate(Z, If[15.5 < g ≤ 16.5, ((-(g - 15.5)) * π), (-π)], U) → Z'
  106. Rotate(W', If[15.5 < g ≤ 16.5, ((-(g - 15.5)) * π), (-π)], U) → W''
  107. Segment(Z', W'') → p_2