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Animation Demonstrating Right Triangle and Incircle

Animation Demonstrating Right Triangle and Incircle
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2017-05-26 22:15
TriangleCircleGeometric Construction
This example dynamically illustrates the properties of an incircle within a right triangle through animation. It covers core concepts like incircles, right triangles, quadratic equations, functions, and geometric transformations. Constructed using commands such as Ray, Point, Segment, Line, Circle, Rotate, and Dilate in GeoGebra, it is suitable for high school mathematics education to explore geometric transformations and their relation to function graphs.

GeoGebra Commands & Parameters

  1. Ray(A, B) → g
  2. Point(g) → F
  3. Ray(A, F) → h
  4. Point(h) → G
  5. Segment(A, G) → k
  6. Line(A, B) → a
  7. OrthogonalLine(A, a) → d
  8. Point(d) → E
  9. Ray(A, E) → i
  10. Point(i) → H
  11. Line(A, H) → m
  12. Segment(A, H) → j
  13. Circle(A, Min[(0.15 * j), (0.15 * k)]) → p
  14. Intersect(p, m) → O, P
  15. Intersect(p, a) → M, N
  16. OrthogonalLine(B, a) → e
  17. Point(d) → C
  18. Ray(A, C) → c
  19. Ray(A, E) → b
  20. Intersect(p, a, 2) → I
  21. Intersect(p, i, 1) → J
  22. Intersect(p, a, 1) → K
  23. Polygon(A, G, H) → poly1, h_1, a_1, g_1
  24. CircleSector(A, N, P) → q
  25. Rotate(q, If[0 < f ≤ 1, (f * π / 2), π / 2], A) → q'
  26. Rotate(G, 45°, A) → G'
  27. Angle(G, A, G') → α
  28. Angle(H, G, A) → β
  29. Rotate(H, β / 2, G) → H'
  30. Angle(H, G, H') → γ
  31. Ray(G, H') → l
  32. Ray(A, G') → n
  33. Intersect(l, n) → D
  34. Line(H, G) → r
  35. Intersect(r, n) → L
  36. Intersect(l, m) → Q
  37. Dilate(A, If[1 < f ≤ 2, 2 - f, 0], L) → A'
  38. Segment(A, A') → s
  39. Intersect(p, n) → R,
  40. Circle(G, (0.15 * Distance[A, G])) → t
  41. Intersect(t, r) → S, T
  42. Intersect(t, l) → U,
  43. CircleSector(G, S, U) → d_1
  44. CircleSector(A, R, P) → c_1
  45. Dilate(G, If[2 < f ≤ 3, 3 - f, 0], D) → G'_1
  46. Segment(G, G'_1) → f_1
  47. Rotate(c_1, If[3 < f ≤ 4, ((-(f - 3)) * π / 4), ((-π)) / 4], A) → e_1
  48. Rotate(d_1, If[4 < f ≤ 5, ((f - 4) * γ), γ], G) → k_1
  49. OrthogonalLine(D, a) → i_1
  50. Intersect(a, i_1) → V
  51. OrthogonalLine(D, r) → j_1
  52. OrthogonalLine(D, m) → l_1
  53. Intersect(j_1, r) → W
  54. Intersect(l_1, m) → Z
  55. Angle(G, V, D) → δ
  56. Dilate(D, If[5 < f ≤ 6, 6 - f, 0], V) → D'
  57. Segment(D, D') → m_1
  58. Angle(V, D, W) → ε
  59. Angle(W, D, Z) → ζ
  60. Angle(Z, D, V) → η
  61. Rotate(V, If[6 < f ≤ 7, ((f - 6) * ε), ε], D) → V'
  62. CircleArc(D, V, V') → p_1
  63. Rotate(W, If[7 < f ≤ 8, ((f - 7) * ζ), ζ], D) → W'
  64. CircleArc(D, W, W') → q_1
  65. Rotate(Z, If[8 < f ≤ 9, ((f - 8) * π / 2), π / 2], D) → Z'
  66. CircleArc(D, Z, Z') → r_1
  67. Circle(D, V) → s_1
  68. Line(Z, W) → n_1
  69. Intersect(l, n_1) → A_1
  70. Dilate(Z, If[9 < f ≤ 10, 10 - f, 0], W) → Z'_1
  71. Segment(Z, Z'_1) → t_1
  72. Dilate(D, If[10 < f ≤ 11, 11 - f, 0], A_1) → D'_1
  73. Segment(D, D'_1) → b_1
  74. Line(A, f_1) → f_2
  75. Point(f_2) → B_1
  76. Angle(B_1, A, G) → θ
  77. Dilate(A, If[11 < f ≤ 12, 12 - f, 0], A_1) → A'_1
  78. Vector(A, A'_1) → u
  79. Translate(e_1, u) → c_2
  80. Rotate(c_2, If[12 < f ≤ 13, ((-(f - 12)) * θ), (-θ)], A_1) → d_2
  81. Segment(A, H) → g_2
  82. Segment(H, G) → h_2