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三角形的外心与外接圆 by MsBuist

三角形的外心与外接圆 by MsBuist
几何画板及绘图内容加载中，请稍等……
2017-06-13 04:08
测试改名0圆几何作图
本范例动态展示了三角形的外接圆构造过程。核心概念包括外心和外接圆。通过使用GeoGebra命令如Segment, Midpoint, OrthogonalLine等，可以清晰地理解几何作图的步骤。适合初中及以上学生学习几何作图和相关概念。

GeoGebra 命令及参数

  1. Segment(A, B) → f
  2. Segment(B, C_1) → g
  3. Segment(C_1, A) → h
  4. Midpoint(f) → D
  5. Midpoint(h) → E
  6. Midpoint(g) → F
  7. OrthogonalLine(D, f) → i
  8. OrthogonalLine(F, g) → j
  9. OrthogonalLine(E, h) → k
  10. Intersect(k, j) → C
  11. Min(list1) → a
  12. Circle(D, (0.1 * a)) → c
  13. Circle(E, (0.1 * a)) → d
  14. Circle(F, (0.1 * a)) → e
  15. Intersect(c, f, 2) → H
  16. Intersect(c, i) → I, J
  17. Intersect(d, h, 2) → K
  18. Intersect(d, k, 2) → L
  19. Intersect(e, g, 2) → M
  20. Intersect(e, j, 2) → N
  21. CircleSector(D, H, J) → p
  22. CircleSector(F, M, N) → q
  23. CircleSector(E, K, L) → r
  24. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], D) → A'
  25. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], F) → B'
  26. Dilate(C_1, If[4 < b ≤ 5, 5 - b, 0], E) → C'
  27. Segment(A, A') → l
  28. Segment(B, B') → m
  29. Segment(C_1, C') → n
  30. Rotate(A, If[1 < b ≤ 2, ((b - 1) * π), π], D) → A'_1
  31. Rotate(A', If[1 < b ≤ 2, ((b - 1) * π), π], D) → A''
  32. Segment(A'_1, A'') → l'
  33. Rotate(B, If[3 < b ≤ 4, ((b - 3) * π), π], F) → B'_1
  34. Rotate(B', If[3 < b ≤ 4, ((b - 3) * π), π], F) → B''
  35. Segment(B'_1, B'') → m'
  36. Rotate(C_1, If[5 < b ≤ 6, ((b - 5) * π), π], E) → C'_1
  37. Rotate(C', If[5 < b ≤ 6, ((b - 5) * π), π], E) → C''
  38. Segment(C'_1, C'') → n'
  39. Polygon(A, B, C_1) → poly1, c_1, a_1, b_1
  40. Rotate(p, If[6.5 < b ≤ 7.5, ((b - 6.5) * π / 2), π / 2], D) → p'
  41. Rotate(q, If[7.5 < b ≤ 8.5, ((b - 7.5) * π / 2), π / 2], F) → q'
  42. Rotate(r, If[8.5 < b ≤ 9.5, ((b - 8.5) * π / 2), π / 2], E) → r'
  43. Dilate(C, If[10 < b ≤ 11, 11 - b, 0], C_1) → C'_2
  44. Segment(C, C'_2) → s
  45. Angle(C_1, C, A) → α
  46. Angle(A, C, B) → β
  47. Angle(B, C, C_1) → γ
  48. Rotate(C, If[11 < b ≤ 12, ((b - 11) * α), α], C) → C'_3
  49. Rotate(C'_2, If[11 < b ≤ 12, ((b - 11) * α), α], C) → G
  50. Segment(C'_3, G) → s'
  51. Rotate(C'_3, If[12 < b ≤ 13, ((b - 12) * β), β], C) → O
  52. Rotate(G, If[12 < b ≤ 13, ((b - 12) * β), β], C) → G'
  53. Segment(O, G') → s''
  54. Rotate(B, If[13 < b ≤ 14, (((b - 13) * 2) * π), (2 * π)], C) → B'_2
  55. CircleArc(C, B, B'_2) → t
  56. Circle(C, B) → d_1