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圆内接四边形的性质

圆内接四边形的性质
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2019-06-29 05:33
圆多边形角变换几何作图
本GeoGebra范例展示了圆内接四边形的一个直接推论：在任何圆内接四边形中，对角互补。该范例涉及圆、角和多边形等核心数学概念。通过使用Circle、Point、Rotate、CircleArc、Segment、Intersect、CircleSector、Dilate、Vector、Translate、Angle、Ray、Polygon等GeoGebra命令，学生可以直观地理解圆内接四边形的性质。适合初中及以上学生学习几何作图。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Rotate(C, 2°, A) → C'
  4. CircleArc(A, C', C) → d
  5. Point(d) → D
  6. CircleArc(A, D, C) → e
  7. Point(e) → E
  8. CircleArc(A, E, C) → f
  9. Point(f) → F
  10. CircleArc(A, F, C) → g
  11. Point(g) → G
  12. Segment(D, E) → b
  13. Segment(E, F) → h
  14. Segment(D, G) → a
  15. Segment(G, F) → i
  16. Circle(F, (0.2 * Distance[A, B])) → k
  17. Circle(E, (0.2 * Distance[A, B])) → p
  18. Circle(G, (0.2 * Distance[A, B])) → q
  19. Circle(D, (0.2 * Distance[A, B])) → r
  20. Intersect(k, i, 1) → H
  21. Intersect(k, h, 1) → I
  22. Intersect(p, h, 1) → J
  23. Intersect(p, b, 1) → K
  24. Intersect(r, a, 1) → L
  25. Intersect(r, b, 1) → M
  26. Intersect(q, a, 1) → N
  27. Intersect(q, i, 1) → O
  28. CircleSector(G, N, O) → s
  29. CircleSector(F, H, I) → t
  30. CircleSector(E, J, K) → c_1
  31. CircleSector(D, M, L) → d_1
  32. Circle(A, B) → e_1
  33. Dilate(E, If[0 < j ≤ 1, 1 - j, 0], G) → E'
  34. Vector(E, E') → u
  35. Translate(c_1, u) → f_1
  36. CircleArc(E, J, K) → g_1
  37. Translate(J, u) → J'
  38. Angle(O, G, J') → α
  39. Rotate(f_1, If[1 < j ≤ 2, ((-(j - 1)) * α), (-α)], G) → h_1
  40. Ray(D, G) → l
  41. Point(l) → P
  42. Ray(G, P) → m
  43. Dilate(F, If[2 < j ≤ 3, 3 - j, 0], D) → F'
  44. Vector(F, F') → v
  45. Ray(G, D) → n
  46. Point(n) → Q
  47. Ray(D, Q) → a_1
  48. Translate(t, v) → t'
  49. CircleArc(F, H, I) → k_1
  50. Translate(I, v) → I'
  51. Angle(I', D, M) → β
  52. Rotate(t', If[3 < j ≤ 4, ((j - 3) * β), β], D) → t''
  53. Polygon(G, D, E, F) → poly1, g_2, d_2, e_2, f_2