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Triangle Cycle 6

Triangle Cycle 6
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2016-10-18 23:14
TriangleCircleCoordinate GeometryGeometric Construction
This example demonstrates a dynamic construction of a triangle cycle, generating a series of triangles through intersections of circles and lines. Core mathematical concepts include circles, line segments, intersection points, triangle construction, and coordinate geometry. The construction uses GeoGebra commands such as Circle, Line, Intersect, and Segment. Suitable for high school mathematics teaching to illustrate geometric constructions and dynamic geometric phenomena.

GeoGebra Commands & Parameters

  1. Circle(O, A) → c
  2. Line(O, A) → f
  3. Circle(A, O) → d
  4. Intersect(d, f, 2) → A'
  5. Circle(O, A') → e
  6. Circle(A', O) → g
  7. Intersect(e, g, 2) → C'
  8. Intersect(e, g, 1) → D'
  9. Line(C', O) → h
  10. Intersect(e, h, 2) → E'
  11. Segment(C', E') → i
  12. Intersect(c, i, 1) → C
  13. Intersect(c, i, 2) → E
  14. Line(D', O) → j
  15. Intersect(e, j, 2) → F'
  16. Segment(D', F') → k
  17. Intersect(c, k, 2) → F
  18. Intersect(c, k, 1) → D
  19. Intersect(c, f, 2) → B
  20. Intersect(e, f, 2) → B'
  21. Segment(A, D') → m
  22. Segment(A', E') → l
  23. Intersect(m, l) → G
  24. Segment(D', B') → n
  25. Segment(A', G) → p
  26. Segment(D, E') → q
  27. Segment(G, D) → r
  28. Segment(E', F') → s
  29. Intersect(n, q) → H
  30. Segment(D', H) → t
  31. Segment(E, B') → a
  32. Segment(B', C') → b
  33. Intersect(s, b) → I
  34. Intersect(s, a) → K
  35. Segment(E', K) → f_1
  36. Segment(B, F') → g_1
  37. Segment(F', A') → h_1
  38. Intersect(b, g_1) → J
  39. Segment(B', J) → i_1
  40. Segment(F, C') → j_1
  41. Intersect(h_1, j_1) → L
  42. Segment(F', L) → k_1
  43. Segment(C, A') → l_1
  44. Segment(C', A) → m_1
  45. Intersect(m_1, l_1) → M
  46. Segment(C', M) → n_1
  47. Segment(A, E) → p_1
  48. Segment(C, D) → q_1
  49. Intersect(q_1, p_1) → N
  50. Segment(C, N) → r_1
  51. Segment(D, N) → s_1
  52. Segment(F, A) → t_1
  53. Segment(C, B) → a_1
  54. Intersect(t_1, r_1) → P
  55. Segment(F, P) → b_1
  56. Intersect(a_1, b_1) → Q
  57. Segment(F, E) → c_1
  58. Segment(Q, B) → d_1
  59. Intersect(c_1, d_1) → R
  60. Segment(B, D) → e_1
  61. Segment(R, E) → f_2
  62. Intersect(f_2, e_1) → S
  63. Segment(D, S) → g_2
  64. Segment(A', A) → h_2
  65. Intersect(p_1, g_2) → T
  66. Segment(A, T) → i_2
  67. Segment(A, T) → j_2