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Dynamic Geometry Problem Example by Tim Brzezinski

Dynamic Geometry Problem Example by Tim Brzezinski
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2017-02-21 00:58
CircleTransformationGeometric Construction
This is a dynamic and modifiable geometry problem example posted by Antonino Gutierrez on Twitter. It demonstrates the dynamic relationships between circles, semicircles, points, line segments, and other geometric elements. Using GeoGebra commands such as Circle, Semicircle, Point, Segment, etc., it provides a clear understanding of geometric transformations and construction. Suitable for high school geometry learners and teachers.

GeoGebra Commands & Parameters

  1. Circle(A_1, A) → c
  2. Circle(C, A) → d
  3. Semicircle(A, D_1) → e
  4. Semicircle(D_1, A) → f
  5. Point(e) → D
  6. Segment(A, D) → g
  7. Intersect(d, g, 2) → P
  8. OrthogonalLine(D, h) → i
  9. Intersect(d, i, 2) → F
  10. Intersect(h, i) → E
  11. Ray(A, F) → j
  12. Intersect(e, j, 2) → G
  13. OrthogonalLine(G, h) → k
  14. Intersect(d, k, 2) → M
  15. Segment(A, M) → l
  16. Intersect(i, l) → N
  17. Distance(A, g) → distanceAg
  18. Distance(A, N) → distanceAN
  19. Distance(P, A) → distancePA
  20. Dilate(A, If[0 < m ≤ 1, 1 - m, 0], P) → A'
  21. Segment(A, A') → n
  22. Dilate(P, If[1 < m ≤ 2, 2 - m, 0], D) → P'
  23. Segment(P, P') → p
  24. Dilate(D, If[2 < m ≤ 3, 3 - m, 0], F) → D'
  25. Segment(D, D') → q
  26. Intersect(k, xAxis) → B
  27. Angle(G, B, A) → β
  28. Angle(D, E, A) → α
  29. Dilate(F, If[3 < m ≤ 4, 4 - m, 0], E) → F'
  30. Segment(F, F') → r
  31. Dilate(A, If[4 < m ≤ 5, 5 - m, 0], F) → A'_1
  32. Segment(A, A'_1) → s
  33. Dilate(F, If[5 < m ≤ 6, 6 - m, 0], G) → F'_1
  34. Segment(F, F'_1) → t
  35. Dilate(G, If[6 < m ≤ 7, 7 - m, 0], M) → G'
  36. Segment(G, G') → f_1
  37. Dilate(M, If[7 < m ≤ 8, 8 - m, 0], B) → M'
  38. Segment(M, M') → g_1
  39. Dilate(A, If[8 < m ≤ 9, 9 - m, 0], N) → A'_2
  40. Segment(A, A'_2) → h_1
  41. Dilate(N, If[9 < m ≤ 10, 10 - m, 0], M) → N'
  42. Segment(N, N') → i_1
  43. Intersect(e, j_1, 1) → I
  44. Angle(N, A, P) → γ
  45. Rotate(A, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → A'_3
  46. Rotate(A'_2, If[11 < m ≤ 12, ((m - 11) * γ), γ], A) → J
  47. Segment(A'_3, J) → k_1
  48. Semicircle(A, H) → c_1
  49. Line(P, N) → l_1
  50. Line(D, M) → m_1
  51. Line(P, D) → n_1
  52. Circle(D, 2) → d_1
  53. Intersect(d_1, n_1, 2) → K
  54. Ray(D, K) → p_1
  55. Intersect(l_1, s) → L
  56. Circle(P, (0.5 * Distance[P, L])) → e_1
  57. Intersect(e_1, k_1, 1) → O
  58. Intersect(e_1, l_1, 2) → Q
  59. Intersect(e_1, l_1, 1) → R
  60. Ray(P, R) → q_1
  61. Circle(D, 2) → r_1
  62. Intersect(r_1, m_1, 1) → S
  63. Ray(D, S) → s_1
  64. Dilate(N, If[12 < m ≤ 13, 13 - m, 0], P) → N'_1
  65. Dilate(M, If[12 < m ≤ 13, 13 - m, 0], D) → M'_1
  66. Segment(N, N'_1) → t_1
  67. Segment(M, M'_1) → a_1
  68. Angle(R, P, O) → δ
  69. Rotate(R, If[13 < m ≤ 14, ((m - 13) * δ), δ], P) → R'
  70. CircleSector(P, R, R') → c_2
  71. Dilate(P, If[14 < m ≤ 15, 15 - m, 0], D) → P'_1
  72. Vector(P, P'_1) → u
  73. Translate(c_2, u) → d_2
  74. Segment(A, D_1) → b_1

AI Drawing Prompt Reference

Draw a dynamic geometry diagram featuring two circles, two semicircles, several points, and line segments. Start by constructing a circle and its semicircles, then create new points and segments using intersections and perpendicular lines. Perform a series of similarity transformations, including dilation and rotation, to observe the dynamic changes in the figure. The final diagram should illustrate the complex relationships and transformations among the geometric elements.
The prompt above was compiled from the original drawing commands and is for reference only.