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Animation 258: Incircle of an Equilateral Triangle

Animation 258: Incircle of an Equilateral Triangle
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2017-05-15 09:21
TriangleCirclePolygonGeometric ConstructionSlider Animation
This example demonstrates the incircle of an equilateral triangle. The core mathematical concepts include triangles, incircles, and equilateral triangles. Using GeoGebra commands such as Polygon, Centroid, Tangent, and Dilate, the construction of an equilateral triangle and its incircle is illustrated. Suitable for middle and high school students to learn about geometric constructions and incircles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 3) → poly1, f, g, h, C
  2. Segment(A, B) → i
  3. Segment(B, C) → j
  4. Segment(C, A) → k
  5. Centroid(poly1) → D
  6. OrthogonalLine(D, g) → l
  7. OrthogonalLine(D, i) → m
  8. Intersect(l, g) → E
  9. Circle(D, E) → c
  10. Angle(B, A, C) → α
  11. Rotate(B, 30°, A) → B'
  12. Angle(B, A, B') → β
  13. Line(A, B') → n
  14. Intersect(c, n, 1) → F
  15. Midpoint(A, F) → G
  16. Tangent(F, c) → p,
  17. Intersect(p, i) → H
  18. Intersect(p, h) → I
  19. Polygon(A, H, I) → poly2, i_1, a, h_1
  20. Centroid(poly2) → J
  21. Circle(J, F) → d
  22. Intersect(c, m, 2) → K
  23. Tangent(K, c) → q,
  24. Intersect(q, g) → L
  25. Intersect(q, h) → M
  26. Polygon(M, L, C) → poly3, c_1, m_1, l_1
  27. Centroid(poly3) → N
  28. Line(B, D) → r
  29. Intersect(h, k) → O
  30. Intersect(r, h) → P
  31. Intersect(c, r) → Q, R
  32. Tangent(Q, c) → s,
  33. Intersect(s, g) → S
  34. Intersect(s, i) → T
  35. Polygon(T, B, S) → poly4, s_1, t, b
  36. Centroid(poly4) → U
  37. Circle(U, Q) → d_1
  38. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], B) → A'
  39. Segment(A, A') → a_1
  40. Rotate(A, If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A'_1
  41. Rotate(A', If[1 < o ≤ 2, ((o - 1) * π / 3), π / 3], A) → A''
  42. Segment(A'_1, A'') → b_1
  43. Rotate(A, If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → A'_2
  44. Rotate(A', If[2 < o ≤ 3, ((-(o - 2)) * π / 3), ((-π)) / 3], B) → A''_1
  45. Segment(A'_2, A''_1) → e_1
  46. Intersect(d, dd, 1) → W_1
  47. Intersect(dd, a_1) → Z_1, A_1
  48. Intersect(ddd, a_1) → A_2, B_1
  49. Center(cc) → B_2
  50. OrthogonalLine(B_2, e_1) → k_3
  51. Intersect(k_3, e_1) → C_2
  52. Angle(B_2, C_2, B) → ι
  53. Tangent(C_2, dd) → l_3, m_3
  54. Intersect(dd, l_3) → V
  55. Center(dd) → C_1
  56. Center(ddd) → D_1
  57. Dilate(B_2, If[3.5 < o ≤ 4.5, 4.5 - o, 0], C_2) → E_1
  58. Dilate(C_1, If[3.5 < o ≤ 4.5, 4.5 - o, 0], A_1) → F_1
  59. Dilate(D_1, If[3.5 < o ≤ 4.5, 4.5 - o, 0], A_2) → G_1
  60. Segment(B_2, E_1) → f_1
  61. Segment(D_1, G_1) → g_1
  62. Segment(C_1, F_1) → j_1
  63. Angle(C_1, V, C_2) → δ
  64. OrthogonalLine(C_1, a_1) → k_1
  65. Intersect(k_1, a_1) → H_1
  66. Angle(C_1, H_1, A) → γ
  67. OrthogonalLine(D_1, a_1) → n_1
  68. Intersect(n_1, a_1) → I_1
  69. Angle(B, I_1, D_1) → ε
  70. Dilate(C_1, If[4.5 < o ≤ 5.5, 5.5 - o, 0], V) → K_1
  71. Segment(C_1, K_1) → p_1
  72. Dilate(C_2, If[5.5 < o ≤ 6.5, 6.5 - o, 0], V) → L_1
  73. Segment(C_2, L_1) → q_1
  74. Dilate(H_1, If[5.5 < o ≤ 6.5, 6.5 - o, 0], I_1) → M_1
  75. Dilate(V, If[6.5 < o ≤ 7.5, 7.5 - o, 0], C_1) → V'
  76. Vector(V, V') → u
  77. Translate(C_2, u) → W
  78. Translate(L_1, u) → Z
  79. Segment(W, Z) → e
  80. Line(A, B) → r_1
  81. Line(V, r_1) → t_1
  82. Point(t_1) → N_1
  83. Angle(N_1, V, C_2) → ζ
  84. Rotate(W, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * ζ), (-ζ)], C_1) → W'
  85. Rotate(Z, If[7.5 < o ≤ 8.5, ((-(o - 7.5)) * ζ), (-ζ)], C_1) → Z'
  86. Segment(W', Z') → e'