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Geometric Construction Example by HeMan123

Geometric Construction Example by HeMan123
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2017-12-05 22:39
CirclePolygonTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to construct geometric figures using GeoGebra commands, involving core math concepts like integers, probability, trigonometric functions, coordinate geometry, and equilateral triangles. Construction highlights include using commands such as Segment, Circle, Intersect, Rotate, Angle, Ray, and Polygon; suitable for middle school and above learning geometric constructions and coordinate geometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Circle(A, B) → c_1
  3. Circle(B, A) → d_1
  4. Intersect(c_1, d_1, 1) → C
  5. Segment(C, A) → g_1
  6. Segment(B, C) → h_1
  7. Rotate(D, 60°, E) → D'
  8. Angle(D, E, D') → α
  9. Segment(D, E) → i
  10. Segment(E, D') → j
  11. Circle(E, 4) → e_1
  12. Intersect(e_1, i, 1) → F
  13. Intersect(e_1, j, 1) → G
  14. Circle(F, 4) → k
  15. Circle(G, 4) → p
  16. Intersect(k, p, 2) → H
  17. Segment(H, E) → l
  18. Rotate(b_1, 25°, a_1) → c_2
  19. Angle(b_1, a_1, c_2) → β
  20. Segment(b_1, a_1) → m
  21. Segment(c_2, a_1) → n
  22. Circle(a_1, 3) → q
  23. Intersect(q, m, 1) → d_2
  24. Intersect(q, n, 1) → e_2
  25. Ray(g, h) → r
  26. Circle(g, 3) → s
  27. Intersect(s, r, 1) → I
  28. Segment(d_2, e_2) → t
  29. Circle(I, 1.3) → f_1
  30. Intersect(s, f_1, 1) → J
  31. Ray(g, J) → i_1
  32. Segment(a_2, b_2) → j_1
  33. Circle(a_2, 10.088889039873256) → k_1
  34. Circle(b_2, 9.877200634618088) → p_1
  35. Intersect(k_1, p_1, 1) → d_3
  36. Intersect(k_1, p_1, 2) → c_3
  37. Segment(d_3, c_3) → l_1
  38. Intersect(j_1, l_1) → e
  39. Segment(K, L) → m_1
  40. Circle(K, 5.047389082576646) → q_1
  41. Circle(L, 5.148910498455693) → r_1
  42. Intersect(q_1, r_1, 1) → M
  43. Intersect(q_1, r_1, 2) → N
  44. Segment(M, N) → n_1
  45. Intersect(m_1, n_1) → O
  46. Circle(M, 4.353709594752132) → s_1
  47. Circle(O, 4.395072539574817) → t_1
  48. Intersect(s_1, t_1, 2) → P
  49. Intersect(s_1, t_1, 1) → Q
  50. Segment(P, Q) → f_2
  51. Polygon(a, b, c) → t1, t_2, r_2, s_2
  52. Circle(a, 4.9119295041113675) → g_2
  53. Circle(b, 5.204069650512864) → h_2
  54. Circle(c, 4.898031168081163) → k_2
  55. Intersect(g_2, k_2, 1) → U
  56. Intersect(g_2, k_2, 2) → V
  57. Segment(U, V) → i_2
  58. Intersect(h_2, k_2, 2) → W
  59. Intersect(h_2, k_2, 1) → Z
  60. Segment(W, Z) → j_2
  61. Intersect(g_2, h_2, 2) → A_1
  62. Segment(c, A_1) → l_2
  63. Intersect(i_2, j_2) → d
  64. Polygon(R, S, T) → t2, t_3, r_3, s_3
  65. Circle(B_1, Radius[Circle[T, R, S]]) → p_2
  66. Circle(c, a, C_1) → q_2