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Dynamic Illustration of External and Internal Tangent Segments

Dynamic Illustration of External and Internal Tangent Segments
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2016-12-16 06:18
CircleTransformationGeometric Construction
In collections Circles (Theorems)
This example dynamically illustrates the relationship between segments created from external and internal tangents of two circles. It involves the geometric properties of circles and the comparison of segment lengths. Using GeoGebra commands such as Circle, Tangent, and Intersect, one can observe the changes in segment lengths under different conditions. Suitable for middle school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Segment(A, B) → f
  3. PointIn(a) → C
  4. Distance(C, c) → b
  5. Circle(C, d) → e
  6. Tangent(c, e) → g, h, i, j
  7. Intersect(c, h) → D
  8. Intersect(c, j) → E, N
  9. Intersect(e, j) → F
  10. Intersect(e, h) → G, L
  11. Intersect(e, g) → H, K
  12. Intersect(e, i) → I
  13. Intersect(c, i) → J, M
  14. Intersect(c, g) → O
  15. Circle(D, 2) → p
  16. Circle(E, 2) → q
  17. Circle(O, 2) → r
  18. Circle(K, 2) → s
  19. Circle(I, 2) → t
  20. Circle(F, 2) → c_1
  21. Circle(G, 2) → d_1
  22. Circle(J, 2) → e_1
  23. Intersect(e_1, i, 1) → P
  24. Intersect(e_1, i, 2) → Q
  25. Intersect(p, h, 1) → R
  26. Intersect(p, h, 2) → S
  27. Intersect(c_1, j, 2) → T
  28. Intersect(c_1, j, 1) → U
  29. Intersect(d_1, h, 1) → V
  30. Intersect(d_1, h, 2) → W
  31. Intersect(s, g, 2) → Z
  32. Intersect(s, g, 1) → A_1
  33. Intersect(r, g, 2) → B_1
  34. Intersect(r, g, 1) → C_1
  35. Intersect(q, j, 2) → D_1
  36. Intersect(q, j, 1) → E_1
  37. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], D) → A'
  38. Dilate(A, If[4 < k ≤ 5, 5 - k, 0], M) → A'_1
  39. Dilate(A, If[9 < k ≤ 10, 10 - k, 0], E) → A'_2
  40. Dilate(A, If[0 < k ≤ 1, 1 - k, 0], O) → A'_3
  41. Angle(A, O, C_1) → α
  42. Angle(A, E, E_1) → β
  43. Angle(A, J, Q) → γ
  44. Angle(A, D, S) → δ
  45. Angle(C, K, A_1) → ε
  46. Intersect(t, i, 1) → F_1
  47. Angle(C, I, F_1) → ζ
  48. Angle(C, F, T) → η
  49. Angle(C, G, W) → θ
  50. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], G) → C'
  51. Dilate(C, If[9 < k ≤ 10, 10 - k, 0], F) → C'_1
  52. Dilate(C, If[4 < k ≤ 5, 5 - k, 0], I) → C'_2
  53. Dilate(C, If[0 < k ≤ 1, 1 - k, 0], K) → C'_3
  54. Segment(A, A') → l
  55. Segment(A, A'_1) → m
  56. Segment(A, A'_2) → n
  57. Segment(A, A'_3) → f_1
  58. Segment(C, C') → g_1
  59. Segment(C, C'_1) → h_1
  60. Segment(C, C'_2) → i_1
  61. Segment(C, C'_3) → j_1
  62. Intersect(i, j) → G_1
  63. Intersect(i, j) → H_1
  64. Intersect(h, i) → I_1
  65. Intersect(g, j) → J_1
  66. Intersect(g, i) → K_1
  67. Intersect(h, j) → L_1
  68. Segment(I_1, M) → k_1
  69. Segment(M, I) → l_1
  70. Segment(I, K_1) → m_1
  71. Segment(J_1, E) → n_1
  72. Segment(E, F) → p_1
  73. Segment(F, L_1) → q_1
  74. Dilate(K_1, If[1 < k ≤ 2, 2 - k, 0], M) → M_1
  75. Dilate(M, If[2 < k ≤ 3, 3 - k, 0], I) → M'
  76. Dilate(I, If[3 < k ≤ 4, 4 - k, 0], I_1) → I'
  77. Segment(K_1, M_1) → r_1
  78. Segment(M, M') → s_1
  79. Segment(I, I') → t_1
  80. Midpoint(M, I) → N_1
  81. Rotate(K_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → O_1
  82. Rotate(M_1, If[5 < k ≤ 6, ((k - 5) * π), π], N_1) → P_1
  83. Segment(O_1, P_1) → a_1
  84. Dilate(J_1, If[6 < k ≤ 7, 7 - k, 0], F) → Q_1
  85. Dilate(F, If[7 < k ≤ 8, 8 - k, 0], E) → F'
  86. Dilate(E, If[8 < k ≤ 9, 9 - k, 0], L_1) → E'
  87. Segment(J_1, Q_1) → b_1
  88. Segment(F, F') → f_2
  89. Segment(E, E') → g_2
  90. Midpoint(Q_1, E) → R_1
  91. Rotate(J_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → S_1
  92. Rotate(Q_1, If[10 < k ≤ 11, ((k - 10) * π), π], R_1) → T_1
  93. Segment(S_1, T_1) → h_2