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米奇定理动态演示

米奇定理动态演示
几何画板及绘图内容加载中，请稍等……
2017-08-07 07:39
圆角几何作图
这是一个动态可修改的“米奇定理”示例。该定理涉及圆和角度的性质。通过点、线、圆、切线等基本几何对象的构造，展示了定理的几何意义。适合初中及以上学生学习几何作图和圆的相关性质。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Line(A, D) → f
  5. Line(A, C) → g
  6. Circle(D, 2) → d
  7. Circle(C, 2) → e
  8. Intersect(e, g, 2) → E
  9. Intersect(d, f, 2) → F
  10. Ray(D, F) → h
  11. Ray(C, E) → i
  12. Point(i) → G
  13. Point(h) → I
  14. Circle(G, C) → k
  15. Circle(I, D) → p
  16. Tangent(k, p) → j, l, m, n
  17. Intersect(-15.601407171722501x² - 1.3443720015595133x y + 0.9727833902891139y² + 24.520011764711146x - 10.706007966687965y = -25.15643549470964, k) → , , ,
  18. Intersect(k, l) → H
  19. Intersect(p, l) → J
  20. OrthogonalLine(H, l) → q
  21. OrthogonalLine(J, l) → r
  22. Line(J, D) → s
  23. Line(H, C) → t
  24. Intersect(s, t) → K
  25. Line(A, K) → a
  26. OrthogonalLine(K, a) → b
  27. Intersect(l, a) → L
  28. Intersect(q, b) → M
  29. Intersect(b, r) → N
  30. Angle(G, H, L) → α
  31. Angle(L, J, I) → β
  32. Angle(A, L, J) → γ
  33. Angle(A, K, M) → δ
  34. Dilate(I, If[0 < o ≤ 1, 1 - o, 0], J) → I'
  35. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], H) → G'
  36. Segment(G, G') → f_1
  37. Segment(I, I') → g_1
  38. Dilate(H, If[1 < o ≤ 2, 2 - o, 0], C) → H'
  39. Dilate(J, If[1 < o ≤ 2, 2 - o, 0], D) → J'
  40. Segment(H, H') → h_1
  41. Segment(J, J') → i_1
  42. Dilate(D, If[2 < o ≤ 3, 3 - o, 0], K) → D'
  43. Dilate(C, If[2 < o ≤ 3, 3 - o, 0], K) → C'
  44. Segment(D, D') → j_1
  45. Segment(C, C') → k_1
  46. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], K) → A'
  47. Segment(A, A') → l_1
  48. Dilate(A, If[4 < o ≤ 5, 5 - o, 0], L) → A'_1
  49. Segment(A, A'_1) → m_1
  50. Segment(G, C) → n_1
  51. Segment(I, D) → p_1
  52. Segment(A, B) → q_1