完全四边形与圆的构造

完全四边形与圆的构造
几何画板及绘图内容加载中,请稍等……
2018-04-17 11:19
本范例展示了通过完全四边形的交点和中点构造的三个圆。它涉及几何作图的核心概念,包括线、交点、中点和圆的构造。使用了GeoGebra中的Line, Intersect, Segment, Midpoint, Circle等命令。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. Line(D, A) → f
  2. Line(A, C) → g
  3. Line(C, B) → h
  4. Line(B, A) → i
  5. Line(D, C) → j
  6. Line(D, B) → k
  7. Intersect(f, h) → I_{AD∧BC}
  8. Intersect(k, g) → I_{AC∧BD}
  9. Intersect(j, i) → I_{AB∧CD}
  10. Segment(A, B) → r
  11. Segment(A, I_{AC∧BD}) → n
  12. Segment(B, I_{AD∧BC}) → p
  13. Midpoint(A, D) → M_{AD}
  14. Midpoint(D, B) → M_{BD}
  15. Midpoint(C, D) → M_{CD}
  16. Midpoint(A, B) → M_{AB}
  17. Midpoint(A, C) → M_{AC}
  18. Midpoint(C, B) → M_{BC}
  19. Segment(D, B) → m
  20. Segment(B, I_{AC∧BD}) → s
  21. Segment(D, A) → l
  22. Segment(D, C) → q
  23. Segment(C, I_{AB∧CD}) → a
  24. Circle(I_{AD∧BC}, M_{AD}, M_{BC}) → c
  25. Circle(I_{AC∧BD}, M_{BD}, M_{AC}) → d
  26. Circle(I_{AB∧CD}, M_{AB}, M_{CD}) → e
  27. Segment(I_{AC∧BD}, C) → b
  28. Segment(C, I_{AD∧BC}) → f_1
  29. Segment(A, I_{AB∧CD}) → t
  30. Segment(A, I_{AD∧BC}) → h_1
  31. Conic(M_{BD}, M_{BC}, M_{AC}, M_{AD}, I_{AB∧CD}) → p9
  32. Intersect(d, c) → I_{dc}1, I_{dc}2, ,
  33. Line(I_{dc}1, I_{dc}2) → Rx_{dc}
  34. Intersect(e, c) → I_{ec}1, I_{ec}2, ,
  35. Line(I_{ec}1, I_{ec}2) → Rx_{ec}
  36. Intersect(e, d) → I_{ed}1, I_{ed}2, ,
  37. Line(I_{ed}2, I_{ed}1) → Rx_{ed}
  38. Intersect(Rx_{ed}, Rx_{dc}) → Rc