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圆内接四边形对角

圆内接四边形对角
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2016-09-27 14:29
圆多边形角变换几何作图
这个范例演示了圆内接四边形的对角性质。核心数学概念包括圆内接四边形的对角互补。作图要点包括使用圆、点、旋转、圆弧、线段、交点、圆扇形、多边形、放大、向量、平移、直线和角度等GeoGebra命令。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) → E
  3. Rotate(E, 1.5707963267948966, A) → E'
  4. Rotate(E', 1.5707963267948966, A) → E''
  5. Rotate(E'', 1.5707963267948966, A) → E'''
  6. CircleArc(A, E, E') → d
  7. CircleArc(A, E', E'') → e
  8. CircleArc(A, E'', E''') → f
  9. CircleArc(A, E''', E) → g
  10. Point(d) → C
  11. Point(e) → D
  12. Point(f) → F
  13. Point(g) → G
  14. Segment(D, C) → a
  15. Segment(C, G) → b
  16. Segment(G, F) → h
  17. Segment(F, D) → i
  18. Circle(D, 1) → k
  19. Circle(C, 1) → p
  20. Circle(G, 1) → q
  21. Circle(F, 1) → r
  22. Intersect(k, i, 1) → H
  23. Intersect(k, a, 1) → I
  24. Intersect(p, a, 1) → J
  25. Intersect(p, b, 1) → K
  26. Intersect(q, b, 1) → L
  27. Intersect(q, h, 1) → M
  28. Intersect(r, h, 1) → N
  29. Intersect(r, i, 1) → O
  30. CircleSector(C, J, K) → s
  31. CircleSector(G, L, M) → t
  32. CircleSector(F, N, D) → c_1
  33. CircleSector(D, H, I) → d_1
  34. Polygon(F, G, C, D) → poly1, f_1, g_1, c_2, d_2
  35. Dilate(D, If[0 < j < 1, 1 - j, 1], G) → D'
  36. Vector(D, D') → u
  37. Dilate(C, If[1 < j < 2, 2 - j, 1], F) → C'
  38. Vector(C, C') → v
  39. Translate(d_1, u) → e_1
  40. Line(D, b) → l
  41. Vector(D, G) → w
  42. Point(l) → P
  43. Angle(I, D, P) → α
  44. Rotate(d_1, α, D) → h_1
  45. Translate(h_1, w) → k_1
  46. Translate(d_1, u) → p_1
  47. Line(F, G) → m
  48. Translate(d_1, u) → q_1
  49. Rotate(q_1, If[0 < j < 1, (j * α), α], D') → r_1
  50. Translate(s, v) → s'
  51. Line(C, i) → n
  52. Point(n) → Q
  53. Angle(Q, C, J) → β
  54. Rotate(s', If[1 < j < 2, ((-(j - 1)) * β), β], C') → s''
  55. Vector(C, F) → u_1
  56. Translate(s, u_1) → s'_1
  57. Rotate(s'_1, (-β), F) → s_1