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三角形中的圆 - 组合几何

三角形中的圆 - 组合几何
几何画板及绘图内容加载中，请稍等……
2020-06-16 12:48
测试改名0圆几何作图
本范例展示了三角形中圆的组合几何问题。核心数学概念包括组合几何、圆的性质和三角形的性质。通过使用GeoGebra命令如Polygon、Circle、Intersect等，可以构造出多个圆与三角形的关系。适合高中数学教学和学习，特别是几何和组合几何部分。

GeoGebra 命令及参数

  1. Polygon(C_{c7}, C_{c10}, 3) → poly1, f, g, h, C_{c1}
  2. Midpoint(h) → D
  3. Midpoint(g) → E
  4. Midpoint(f) → F
  5. Circle(C_{c7}, 1) → c_7gray
  6. Circle(C_{c1}, 1) → c_1orange
  7. Circle(C_{c10}, 1) → c_{10}gray
  8. Intersect(c_1orange, h, 1) → G
  9. Intersect(c_1orange, g, 1) → H
  10. Intersect(c_{10}gray, g, 1) → I
  11. Intersect(c_7gray, f, 1) → J
  12. Intersect(c_7gray, h, 1) → K
  13. Intersect(c_{10}gray, f, 1) → L
  14. Midpoint(J, F) → C_{c8}
  15. Circle(C_{c8}, 1) → c_8gray
  16. Midpoint(F, L) → C_{c9}
  17. Midpoint(I, E) → C_{c6}
  18. Midpoint(E, H) → C_{c3}
  19. Midpoint(G, D) → C_{c2}
  20. Midpoint(D, K) → C_{c4}
  21. Circle(C_{c2}, 1) → c_2orange
  22. Circle(C_{c4}, 1) → c_4gray
  23. Circle(C_{c3}, 1) → c_3gray
  24. Circle(C_{c6}, 1) → c_6gray
  25. Circle(C_{c9}, 1) → c_9gray
  26. Midpoint(C_{c4}, C_{c6}) → C_{c5}
  27. Circle(C_{c5}, 1) → c_5gray
  28. Line(A, B) → i
  29. Rotate(B, 120°, C_{c10}) → B'
  30. Rotate(A, (-(120°)), C_{c7}) → A'
  31. Tangent(A', c_7gray) → j,
  32. Tangent(B', c_{10}gray) → k,
  33. Intersect(j, k) → C
  34. Intersect(i, j) → M
  35. Intersect(i, k) → N
  36. Polygon(M, N, C) → t1, c_{11}, m, n
  37. Circle(C_{c2}, 1) → c_2purple
  38. Circle(C_{c2}, 1) → c_2green
  39. Circle(C_{c2}, 1) → c_2gray
  40. Circle(C_{c1}, 1) → c_1gray
  41. Circle(C_{c1}, 1) → c_1purple
  42. Circle(C_{c1}, 1) → c_1green
  43. Circle(C_{c3}, 1) → c_3orange
  44. Circle(C_{c3}, 1) → c_3green
  45. Circle(C_{c3}, 1) → c_3purple
  46. Circle(C_{c4}, 1) → c_4orange
  47. Circle(C_{c4}, 1) → c_4green
  48. Circle(C_{c4}, 1) → c_4purple
  49. Circle(C_{c5}, 1) → c_5orange
  50. Circle(C_{c5}, 1) → c_5green
  51. Circle(C_{c5}, 1) → c_5purple
  52. Circle(C_{c6}, 1) → c_6green
  53. Circle(C_{c6}, 1) → c_6purple
  54. Circle(C_{c6}, 1) → c_6orange
  55. Circle(C_{c7}, 1) → c_7orange
  56. Circle(C_{c7}, 1) → c_7green
  57. Circle(C_{c7}, 1) → c_7purple
  58. Circle(C_{c8}, 1) → c_8green
  59. Circle(C_{c8}, 1) → c_8orange
  60. Circle(C_{c8}, 1) → c_8purple
  61. Circle(C_{c9}, 1) → c_9green
  62. Circle(C_{c9}, 1) → c_9purple
  63. Circle(C_{c9}, 1) → c_9orange
  64. Circle(C_{c10}, 1) → c_{10}green
  65. Circle(C_{c10}, 1) → c_{10}purple
  66. Circle(C_{c10}, 1) → c_{10}orange