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GoGeometry Action 3

GoGeometry Action 3
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2017-02-23 04:22
TriangleVectorGeometric Construction
This is a dynamic and modifiable geometric problem example posted by Antonino Gutierrez on Twitter. It demonstrates a tangent line problem in triangles. Using GeoGebra commands such as Ray, Rotate, Angle, Point, etc., one can dynamically explore and understand the properties of geometric figures. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, (a * π / 180), A) → B'
  3. Angle(B, A, B') → α
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Point(f) → D
  7. Segment(C, D) → h
  8. Segment(A, D) → i
  9. Segment(A, C) → j
  10. Circle(C, 4) → c
  11. Circle(D, 4) → d
  12. Intersect(c, g, 2) → E
  13. Intersect(d, f, 2) → F
  14. Ray(D, F) → k
  15. Ray(C, E) → l
  16. Min({i, j}) → b
  17. Circle(C, (0.15 * b)) → e
  18. Circle(D, (0.15 * b)) → p
  19. Angle(F, D, C) → β
  20. Angle(D, C, E) → γ
  21. Rotate(F, β / 2, D) → F'
  22. Angle(F, D, F') → δ
  23. Rotate(D, γ / 2, C) → D'
  24. Angle(D, C, D') → ε
  25. Ray(C, D') → m
  26. Ray(D, F') → n
  27. Intersect(e, m, 1) → G
  28. Intersect(e, h, 1) → H
  29. Intersect(p, h, 1) → I
  30. CircleSector(C, H, G) → q
  31. CircleSector(D, F, F') → r
  32. Intersect(m, n) → J
  33. OrthogonalLine(J, k) → s
  34. OrthogonalLine(J, l) → t
  35. Intersect(s, k) → K
  36. Intersect(t, l) → L
  37. Circle(J, K) → c_1
  38. Segment(L, K) → f_1
  39. Midpoint(f_1) → M
  40. OrthogonalLine(M, f_1) → g_1
  41. Intersect(c_1, g_1, 2) → N
  42. Segment(N, C) → h_1
  43. Segment(N, D) → i_1
  44. Intersect(f_1, h_1) → O
  45. Segment(L, O) → j_1
  46. Circle(O, j_1) → d_1
  47. Intersect(d_1, f_1, 2) → P
  48. Polygon(A, D, C) → poly1, c_2, a_1, d_2
  49. Angle(J, K, D) → ζ
  50. Angle(C, L, J) → η
  51. Intersect(f_1, i_1) → Q
  52. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], D) → A'
  53. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], C) → A'_1
  54. Segment(A, A') → k_1
  55. Segment(A, A'_1) → l_1
  56. Dilate(C, If[1 < o ≤ 2, 2 - o, 0], J) → C'
  57. Dilate(D, If[1 < o ≤ 2, 2 - o, 0], J) → D'_1
  58. Segment(C, C') → m_1
  59. Segment(D, D'_1) → n_1
  60. Rotate(r, If[2.5 < o ≤ 3.5, ((o - 2.5) * δ), δ], D) → r'
  61. Rotate(q, If[3.5 < o ≤ 4.5, ((o - 3.5) * ε), ε], C) → q'
  62. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], L) → J'
  63. Dilate(J, If[5 < o ≤ 6, 6 - o, 0], K) → J'_1
  64. Segment(J, J'_1) → p_1
  65. Segment(J, J') → q_1
  66. Angle(L, J, K) → θ
  67. Rotate(L, If[6 < o ≤ 7, ((o - 6) * θ), θ], J) → L'
  68. CircleArc(J, L, L') → e_1
  69. Rotate(K, If[7 < o ≤ 8, ((o - 7) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → K'
  70. CircleArc(J, K, K') → r_1
  71. Rotate(N, If[8 < o ≤ 9, ((o - 8) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → N'
  72. CircleArc(J, N, N') → s_1
  73. Rotate(r_1, If[10 < o ≤ 11, ((o - 10) * ((2 * π) - θ) / 2), ((2 * π) - θ) / 2], J) → t_1
  74. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], D) → N'_1
  75. Dilate(N, If[11 < o ≤ 12, 12 - o, 0], C) → N'_2
  76. Segment(N, N'_1) → b_1
  77. Segment(N, N'_2) → f_2
  78. Dilate(L, If[12 < o ≤ 13, 13 - o, 0], O) → L'_1
  79. Dilate(O, If[13 < o ≤ 14, 14 - o, 0], P) → O'
  80. Segment(L, L'_1) → g_2
  81. Segment(O, O') → h_2
  82. Dilate(P, If[14 < o ≤ 15, 15 - o, 0], Q) → P'
  83. Segment(P, P') → i_2
  84. Dilate(Q, If[15 < o ≤ 16, 16 - o, 0], K) → Q'
  85. Segment(Q, Q') → j_2
  86. Rotate(L, If[17 < o ≤ 18, ((o - 17) * π), π], O) → L'_2
  87. Rotate(L'_1, If[17 < o ≤ 18, ((o - 17) * π), π], O) → R
  88. Segment(L'_2, R) → k_2
  89. Rotate(Q, If[18 < o ≤ 19, ((o - 18) * π), π], Q) → Q'_1
  90. Rotate(Q', If[18 < o ≤ 19, ((o - 18) * π), π], Q) → Q''
  91. Segment(Q'_1, Q'') → l_2
  92. Min(c_2, d_2) → w
  93. Circle(A, (0.15 * w)) → e_2
  94. Segment(A, C) → m_2
  95. Intersect(e_2, m_2) → S,
  96. Segment(A, D) → n_2
  97. Intersect(e_2, n_2) → T,
  98. CircleSector(A, T, S) → p_2