积极 AI Logo 积极 AI

直角三角形内切圆与外切圆动态演示

直角三角形内切圆与外切圆动态演示
几何画板及绘图内容加载中，请稍等……
2019-07-31 03:39
测试改名0圆几何作图
①本范例动态演示直角三角形的内切圆与外切圆的几何关系；②涉及核心概念：直角三角形、内切圆、外切圆、切线、旋转、相似三角形；③作图要点：使用 GeoGebra 命令如 Intersect（交点）、Semicircle（半圆）、Polygon（多边形）、Rotate（旋转）、Dilate（缩放）等构建图形；④适合高中数学教学，用于理解特殊四边形与圆的几何性质。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Semicircle(A, B) → c
  3. Point(c) → C
  4. Polygon(A, C, B) → t1, b, a_1, c_1
  5. Angle(B, A, C) → α
  6. Rotate(B, α / 2, A) → B'
  7. Angle(B, A, B') → β
  8. Ray(A, B') → f
  9. Rotate(A, π / 4, C) → A'
  10. Ray(C, A') → g
  11. Ray(A, C) → h
  12. Ray(A, B) → i
  13. Segment(B, C) → j
  14. Intersect(g, f) → D
  15. Ray(B, B + (1, 0, 0)) → k
  16. Point(k) → E
  17. Circle(C, 3) → d
  18. Intersect(d, h, 2) → F
  19. Angle(E, B, C, xOyPlane) → γ
  20. Rotate(E, γ / 2, B) → E'
  21. Ray(B, E') → l
  22. Rotate(B, π / 4, C) → B'_1
  23. Ray(C, B'_1) → m
  24. Intersect(l, m) → G
  25. OrthogonalLine(D, h) → n
  26. OrthogonalLine(D, k, xOyPlane) → p
  27. Intersect(n, h) → H
  28. Intersect(p, i) → I
  29. OrthogonalLine(G, h, xOyPlane) → q
  30. OrthogonalLine(G, k, xOyPlane) → r
  31. Intersect(q, h) → J
  32. Intersect(r, i) → K
  33. Circle(G, J, xOyPlane) → e
  34. Circle(D, H) → s
  35. Ray(B, D) → t
  36. Angle(A, C, B) → δ
  37. Ray(B, D) → f_1
  38. Ray(A, D) → g_1
  39. Min({Distance[A, D], Distance[B, D], Distance[B, G], Distance[C, G]}) → o
  40. Circle(A, (0.35 * o)) → d_1
  41. Intersect(d_1, i) → L,
  42. Circle(B, (0.35 * o)) → e_1
  43. Circle(C, (0.35 * o)) → h_1
  44. Intersect(h_1, h, 2) → M
  45. Intersect(k, e_1) → N,
  46. Intersect(e_1, j) → O,
  47. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], D) → A'_1
  48. Segment(A, A'_1) → i_1
  49. Dilate(B, If[0 < u ≤ 1, 1 - u, 0], D) → B'_2
  50. Segment(B, B'_2) → j_1
  51. Rotate(O, If[0 < u ≤ 1, (u * (π / 2 - α) / 2), (π / 2 - α) / 2], B) → O'
  52. Rotate(L, If[0 < u ≤ 1, (u * β), β], A) → L'
  53. CircleSector(B, O, O') → k_1
  54. CircleSector(A, L, L') → p_1
  55. Dilate(C, If[1 < u ≤ 2, 2 - u, 0], G) → C'
  56. Dilate(B, If[1 < u ≤ 2, 2 - u, 0], G) → B'_3
  57. Segment(B, B'_3) → l_1
  58. Segment(C, C') → m_1
  59. Intersect(h_1, j) → P,
  60. Rotate(P, If[1 < u ≤ 2, ((u - 1) * π / 4), π / 4], C) → P'
  61. Rotate(N, If[1 < u ≤ 2, ((u - 1) * γ / 2), γ / 2], B) → N'
  62. CircleSector(B, N, N', xOyPlane) → q_1
  63. CircleSector(C, P, P') → r_1
  64. Rotate(p_1, If[2.5 < u ≤ 3.5, ((u - 2.5) * β), β], A) → s_1
  65. Rotate(k_1, If[2.5 < u ≤ 3.5, ((u - 2.5) * (π / 2 - α) / 2), (π / 2 - α) / 2], B) → t_1
  66. Rotate(q_1, If[3.5 < u ≤ 4.5, ((u - 3.5) * γ / 2), γ / 2], B) → c_2
  67. Rotate(r_1, If[3.5 < u ≤ 4.5, ((u - 3.5) * π / 4), π / 4], C) → d_2
  68. Dilate(D, If[5 < u ≤ 6, 6 - u, 0], H) → D'
  69. Circle(D, D') → e_2
  70. OrthogonalLine(D, j) → n_1
  71. Intersect(j, n_1) → Q
  72. Dilate(G, If[6 < u ≤ 7, 7 - u, 0], J) → G'
  73. Circle(G, G', xOyPlane) → f_2
  74. OrthogonalLine(G, j, xOyPlane) → b_1
  75. Intersect(b_1, j) → R
  76. Dilate(H, If[12 < u ≤ 13, 13 - u, 0], R) → H'
  77. Dilate(R, If[13 < u ≤ 14, 14 - u, 0], K) → R'
  78. Ray(C, J) → i_2
  79. Segment(A, C) → j_2
  80. Dilate(D, If[16 < u ≤ 17, 17 - u, 0], R) → D'_1
  81. Ray(K, R) → m_2
  82. Ray(J, Q) → n_2
  83. Intersect(m_2, n_2) → U
  84. Dilate(K, If[12 < u ≤ 13, 13 - u, 0], R) → K'
  85. Dilate(J, If[12 < u ≤ 13, 13 - u, 0], Q) → J'
  86. Segment(J, J') → p_2
  87. Segment(K, K') → q_2
  88. Dilate(R, If[13 < u ≤ 14, 14 - u, 0], U) → R'_1
  89. Dilate(Q, If[13 < u ≤ 14, 14 - u, 0], U) → Q'
  90. Segment(Q, Q') → g_2
  91. Segment(R, R'_1) → k_2
  92. Dilate(J, If[14 < u ≤ 15, 15 - u, 0], K) → J'_1
  93. Segment(J, J'_1) → l_2
  94. Polygon(J, U, K) → t2, k_3, j_3, u_1
  95. Dilate(C, If[16 < u ≤ 17, 17 - u, 0], J) → C'_1
  96. Vector(C, C'_1) → v
  97. Translate(d_2, v) → h_2
  98. Line(C, p_2) → r_2
  99. Point(r_2) → S
  100. Angle(S, C, G, xOyPlane) → ε
  101. Rotate(h_2, If[16 < u ≤ 17, ((-(u - 16)) * ε), (-ε)], C'_1) → s_2
  102. Dilate(J, If[18 < u ≤ 19, 19 - u, 0], K) → J'_2
  103. Vector(J, J'_2) → w
  104. Translate(s_2, w) → t_2
  105. Line(K, p_2) → a_2
  106. Point(a_2) → T
  107. Rotate(t_2, If[18 < u ≤ 19, (((-(u - 18)) * 3) * π / 4), (-3 * π / 4)], J'_2) → c_3