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圆与弦的动态关系

圆与弦的动态关系
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2017-04-07 10:12
圆角几何作图
所属专题 Circles (Theorems)
该范例展示了圆中弦与另一个与该弦及原圆相切的圆之间的关系。通过动态调整，可以观察到不同条件下这些圆和弦的变化。涉及的核心数学概念包括圆的性质、切线和弦的关系。使用了GeoGebra中的Circle、Point、Segment、Tangent、Angle、Rotate等命令进行构造。适合初中及以上学生或教师教学使用。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Segment(D, C) → f
  5. CircleArc(A, C, D) → d
  6. Point(d) → E
  7. Tangent(E, c) → g,
  8. Angle(D, A, C) → α
  9. Rotate(D, α / 2, A) → D'
  10. Angle(D, A, D') → β
  11. Segment(D', E) → h
  12. Intersect(f, h) → F
  13. OrthogonalLine(E, g) → i
  14. LineBisector(F, E) → j
  15. Intersect(i, j) → G
  16. Circle(G, F) → e
  17. Circle(D', C) → k
  18. Intersect(e, k, 2) → H
  19. Intersect(e, k, 1) → I
  20. Segment(D', I) → l
  21. Segment(D', H) → m
  22. Angle(G, I, D') → γ
  23. Angle(D', H, G) → δ
  24. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], C) → D'_1
  25. Segment(D, D'_1) → n
  26. Point(g) → J
  27. Angle(J, E, G) → ε
  28. Angle(C, A, D) → ζ
  29. Rotate(C, If[1 < a ≤ 2, ((a - 1) * ζ), ζ], A) → C'
  30. CircleArc(A, C, C') → p
  31. Angle(D, A, D') → θ
  32. Rotate(D, If[2 < a ≤ 3, ((a - 2) * θ), θ], A) → D'_2
  33. CircleArc(A, D, D'_2) → q
  34. Dilate(D, If[3 < a ≤ 4, 4 - a, 0], D') → D'_3
  35. Segment(D, D'_3) → r
  36. Rotate(q, If[4.5 < a ≤ 5.5, ((a - 4.5) * θ), θ], A) → q'
  37. Rotate(D, If[4.5 < a ≤ 5.5, ((a - 4.5) * θ), θ], A) → D'_4
  38. Rotate(D'_3, If[4.5 < a ≤ 5.5, ((a - 4.5) * θ), θ], A) → K
  39. Segment(D'_4, K) → r'
  40. Dilate(G, If[7 < a ≤ 8, 8 - a, 0], E) → G'
  41. Segment(G, G') → s
  42. Rotate(E, If[8 < a ≤ 10, ((a - 8) * π), (2 * π)], G) → E'
  43. CircleArc(G, E, E') → t
  44. Dilate(G, If[7 < a ≤ 8, 8 - a, 0], F) → G'_1
  45. Segment(G, G'_1) → b
  46. Angle(G, F, D) → η
  47. Dilate(D', If[10 < a ≤ 11, 11 - a, 0], I) → D''
  48. Segment(D', D'') → f_1
  49. Dilate(G, If[10 < a ≤ 11, 11 - a, 0], I) → G'_2
  50. Segment(G, G'_2) → g_1
  51. Angle(C, D', I) → ρ
  52. Dilate(DD, If[12.5 < a ≤ 13.5, 13.5 - a, 0], F) → DD'
  53. Dilate(E, If[12 < a ≤ 13, 13 - a, 0], F) → E'_1
  54. Segment(E, E'_1) → h_1
  55. Dilate(F, If[13 < a ≤ 14, 14 - a, 0], D') → F'
  56. Segment(FF, F') → i_1
  57. Rotate(D'_4, If[14 < a ≤ 15, ((a - 14) * ρ), ρ], D') → L
  58. Rotate(K, If[14 < a ≤ 15, ((a - 14) * ρ), ρ], D') → K'
  59. Segment(L, K') → r''