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两圆外切圆心轨迹 by Irina Boyadzhiev

两圆外切圆心轨迹 by Irina Boyadzhiev
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2015-11-19 13:08
圆几何作图轨迹
所属专题 Conic Sections
本范例展示了所有与给定两圆外切的圆的圆心轨迹。核心概念包括圆的性质、轨迹和几何作图。通过使用GeoGebra命令如Circle、Point、Line、Intersect等，可以动态探索圆心轨迹的变化。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Circle(A, B_1) → c
  2. Point(c) → E
  3. Line(A, E) → f
  4. Circle(E, Segment[B, D]) → e
  5. Circle(B, D) → d
  6. Segment(A, E) → a
  7. Intersect(e, f, 1) → M1
  8. LineBisector(M1, B) → b
  9. Segment(M1, B) → h
  10. Intersect(b, f) → O1
  11. Circle(O1, E) → g
  12. Segment(O1, A) → i
  13. Segment(O1, B) → j
  14. Segment(A, B) → k
  15. Intersect(d, k) → C_1,
  16. Intersect(c, k) → H,
  17. Midpoint(H, C_1) → I
  18. Intersect(g, d) → J, G, ,
  19. Segment(O1, E) → l
  20. Segment(O1, J) → m
  21. Segment(B, J) → p
  22. Angle(h, b) → α
  23. Intersect(e, f, 2) → M2
  24. LineBisector(M2, B) → r
  25. Intersect(r, f) → O2
  26. Intersect(f, l) → L
  27. Circle(O2, E) → s
  28. Intersect(s, d) → M, C, ,
  29. Segment(O2, M) → a_1
  30. Segment(O2, E) → b_1
  31. Segment(B, M) → c_1
  32. Segment(A, B) → d_1
  33. Segment(M2, B) → n
  34. Angle(n, r) → β
  35. Locus(O2, E) → loc2
  36. Locus(O1, E) → loc1
  37. Corner(1) → X1
  38. Corner(4) → X4
  39. Midpoint(X1, X4) → XX
  40. Line(XX, xAxis) → e_1
  41. Polygon(XX, (x(Corner[2]), y(XX)), Corner[3], X4) → poly1, xx, f_1, g_1, x4
  42. Midpoint(X1, XX) → XL
  43. Polygon(X1, Corner[2], (x(Corner[2]), y(XX)), XX) → poly2, h_1, i_1, j_1, k_1