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Dynamic Geometry Problem Demonstration

Dynamic Geometry Problem Demonstration
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2018-02-02 12:01
PolygonAngleTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates a geometry problem posted by Antonio Gutierrez on Twitter. It involves core mathematical concepts such as special points, quadratic equations, and polygons. Key construction points include using GeoGebra commands and objects like Circle, Ray, Point, Semicircle, Segment, Polygon, Midpoint, Angle, OrthogonalLine, Intersect, Rotate, Line, Distance, Dilate, Min, and CircleSector. Suitable for high school and above, for learning and exploring geometric problems.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Ray(A, B) → f
  3. Point(f) → C
  4. Semicircle(A, C) → d
  5. Point(d) → D
  6. Segment(A, D) → g
  7. Segment(D, C) → h
  8. Segment(C, A) → i
  9. Polygon(A, C, D) → t1, d_1, a, c_1
  10. Midpoint(A, C) → E
  11. Angle(A, D, C) → α
  12. OrthogonalLine(D, i) → j
  13. Intersect(j, i) → F
  14. Angle(D, F, A) → β
  15. Segment(D, F) → k
  16. Angle(D, C, F) → γ
  17. Angle(F, A, D) → δ
  18. Rotate(F, δ / 2, A) → F'
  19. Angle(F, A, F') → ε
  20. Rotate(D, γ / 2, C) → D'
  21. Angle(D, C, D') → ζ
  22. Ray(A, F') → l
  23. Ray(C, D') → m
  24. Rotate(D, π / 4, F) → D'_1
  25. Angle(D, F, D'_1) → η
  26. Ray(F, D'_1) → n
  27. Rotate(C, π / 4, F) → C'
  28. Angle(C, F, C') → θ
  29. Ray(F, C') → p
  30. Intersect(l, n) → G
  31. Intersect(m, p) → H
  32. OrthogonalLine(G, g) → q
  33. Intersect(g, q) → I
  34. OrthogonalLine(H, i) → r
  35. Intersect(i, xAxis) → J
  36. Intersect(r, i) → K
  37. Line(D, C) → s
  38. Ray(G, H) → t
  39. Intersect(s, t) → L
  40. Distance(G, L) → distanceGL
  41. Distance(F, D) → distanceFD
  42. Distance(D, L) → distanceDL
  43. Distance(D, F) → distanceDF
  44. Dilate(D, If[0 < b ≤ 1, 1 - b, 0], F) → D'_2
  45. Segment(D, D'_2) → e
  46. Dilate(F, If[1 < b ≤ 2, 2 - b, 0], H) → F'_1
  47. Dilate(C, If[1 < b ≤ 2, 2 - b, 0], H) → C'_1
  48. Segment(F, F'_1) → f_1
  49. Segment(C, C'_1) → g_1
  50. Segment(C, L) → h_1
  51. Segment(F, K) → i_1
  52. Intersect(t, e) → M
  53. Segment(F, M) → j_1
  54. Segment(F, A) → k_1
  55. Segment(A, I) → l_1
  56. Min({h_1, i_1, j_1, k_1, l_1}) → o
  57. Circle(C, (0.7 * o)) → e_1
  58. Circle(F, (0.7 * o)) → p_1
  59. Circle(A, (0.7 * o)) → q_1
  60. Intersect(i, xAxis) → N
  61. Intersect(i, xAxis) → O
  62. Intersect(i, xAxis) → P
  63. Intersect(q_1, i) → Q,
  64. Intersect(p_1, i) → R, S
  65. Intersect(p_1, e_1) → T, , ,
  66. Intersect(e_1, s) → U, V
  67. Rotate(U, If[2 < b ≤ 3, ((b - 2) * ζ), ζ], C) → U'
  68. Rotate(R, If[2 < b ≤ 3, ((b - 2) * π / 4), π / 4], F) → R'
  69. CircleSector(C, U, U') → r_1
  70. CircleSector(F, R, R') → s_1
  71. Rotate(r_1, If[4 < b ≤ 5, ((b - 4) * ζ), ζ], C) → t_1
  72. Rotate(s_1, If[4 < b ≤ 5, ((b - 4) * π / 4), π / 4], F) → c_2
  73. Dilate(A, If[5 < b ≤ 6, 6 - b, 0], G) → A'
  74. Dilate(F, If[5 < b ≤ 6, 6 - b, 0], G) → F'_2
  75. Segment(A, A') → m_1
  76. Segment(F, F'_2) → n_1
  77. Rotate(Q, If[6 < b ≤ 7, ((b - 6) * ε), ε], A) → Q'
  78. CircleSector(A, Q, Q') → d_2
  79. Rotate(d_2, If[8 < b ≤ 9, ((b - 8) * ε), ε], A) → e_2
  80. Rotate(c_2, If[8 < b ≤ 9, ((b - 8) * π / 4), π / 4], F) → f_2
  81. Dilate(G, If[9 < b ≤ 10, 10 - b, 0], H) → G'
  82. Segment(G, G') → a_1
  83. Dilate(H, If[10 < b ≤ 11, 11 - b, 0], L) → H'
  84. Segment(H, H') → b_1
  85. Dilate(D, If[11 < b ≤ 12, 12 - b, 0], L) → D'_3
  86. Segment(D, D'_3) → g_2
  87. Angle(F, D, C) → ρ
  88. Rotate(D, If[13 < b ≤ 14, ((b - 13) * ρ), ρ], D) → D'_4
  89. Rotate(D'_2, If[13 < b ≤ 14, ((b - 13) * ρ), ρ], D) → W
  90. Segment(D'_4, W) → e'