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圆内直径与弦的关系

圆内直径与弦的关系
几何画板及绘图内容加载中，请稍等……
2016-05-04 20:55
圆解析几何几何作图
所属专题 Circles (Theorems)
本范例通过互动方式让学生发现：在圆内，如果直径垂直于弦，则该直径会平分弦。核心数学概念包括圆的性质、垂直线段的性质。使用了Circle, Intersect, CircleArc, Point, Segment, OrthogonalLine, Dilate, Rotate, Angle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. Intersect(c, a, 1) → C
  3. Intersect(c, a, 2) → D
  4. CircleArc(A, C, D) → d
  5. Point(d) → E
  6. CircleArc(A, E, D) → e
  7. Point(e) → F
  8. Segment(E, F) → f
  9. OrthogonalLine(A, f) → g
  10. Intersect(g, f) → G
  11. Circle(G, (0.2 * Distance[A, B])) → h
  12. Intersect(h, g, 2) → H
  13. Intersect(h, g, 1) → I
  14. Intersect(h, f, 1) → J
  15. Intersect(h, f, 2) → K
  16. Intersect(c, g, 1) → L
  17. Intersect(c, g, 2) → M
  18. Dilate(E, If[0 < b ≤ 1, 1 - b, 0], F) → E'
  19. Segment(E, E') → i
  20. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], L) → A'
  21. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], M) → A'_1
  22. Segment(A, A'_1) → j
  23. Segment(A, A') → k
  24. CircleArc(A, L, F) → q
  25. CircleArc(A, E, L) → r
  26. Segment(G, F) → l
  27. Segment(E, G) → m
  28. Rotate(G, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 2), 1.5707963267948966], G) → G'_1
  29. Rotate(F, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 2), 1.5707963267948966], G) → F'_1
  30. Rotate(G, If[2.5 < b ≤ 3.5, ((b - 2.5) * π), 3.141592653589793], G) → G'_2
  31. Rotate(F, If[2.5 < b ≤ 3.5, ((b - 2.5) * π), 3.141592653589793], G) → F'_2
  32. Segment(G'_2, F'_2) → l'
  33. Rotate(F, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 2), -1.5707963267948966], A) → F'_3
  34. CircleArc(A, F'_3, F) → t
  35. Angle(L, A, F) → α
  36. Rotate(L, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * α), (-α)], A) → L'
  37. CircleArc(A, E, L') → c_1
  38. Angle(F, G, A) → β
  39. Rotate(q, If[3.5 < b ≤ 4.5, ((-(b - 3.5)) * α), (-α)], A) → q'