MathPlotAI Logo MathPlotAI

Dynamic Illustration of Relationship between 2 Special Secant Segments of a Circ

Dynamic Illustration of Relationship between 2 Special Secant Segments of a Circ
Loading the math board and drawing, please wait…
2017-05-30 04:53
CircleTrigonometryGeometric ConstructionLocus
This example dynamically demonstrates the relationship between two special secant segments in a circle. It involves core mathematical concepts such as circle power theorem, trigonometry, and geometric transformations. The construction utilizes GeoGebra commands like Circle, Point, Line, Intersect, CircleArc, Segment, Rotate, Angle, Ray, Dilate, Vector, Translate, Min, and CircleSector. It is suitable for high school and above students to understand the application of geometric transformations and circle power theorem.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(A, C) → f
  4. Intersect(c, f, 2) → D
  5. CircleArc(A, C, D) → d
  6. CircleArc(A, D, C) → e
  7. Segment(A, C) → g
  8. Circle(D, g) → h
  9. Rotate(C, (3 * π / 4), A) → C'
  10. Angle(C, A, C') → α
  11. Ray(A, C') → j
  12. CircleArc(A, C, C') → k
  13. CircleArc(A, C', D) → p
  14. Point(p) → F
  15. Circle(F, g) → q
  16. Intersect(q, f) → H, I
  17. Dilate(C, If[0 < a ≤ 1, 1 - a, 0], A) → C'_1
  18. Segment(C, C'_1) → i
  19. Dilate(I, If[1 < a ≤ 2, 2 - a, 0], D) → I'
  20. Segment(A, I') → l
  21. Ray(H, F) → m
  22. Intersect(k, m, 1) → E
  23. Dilate(D, If[2 < a ≤ 3, 3 - a, 0], H) → D'
  24. Segment(D, D') → n
  25. Dilate(H, If[3 < a ≤ 4, 4 - a, 0], F) → H'
  26. Segment(H, H') → r
  27. Dilate(F, If[4 < a ≤ 5, 5 - a, 0], E) → F'
  28. Segment(F, F') → s
  29. Angle(C, A, E) → β
  30. Rotate(C, β / 3, A) → C'_2
  31. Angle(C, A, C'_2) → γ
  32. Rotate(C'_2, β / 3, A) → G
  33. Angle(C'_2, A, G) → δ
  34. Ray(A, G) → t
  35. Ray(A, C'_2) → b
  36. Ray(A, E) → f_1
  37. Angle(C, H, E) → ε
  38. Rotate(A, If[5 < a ≤ 6, ((a - 5) * ε), ε], D) → A'
  39. Rotate(I', If[5 < a ≤ 6, ((a - 5) * ε), ε], D) → I''
  40. Segment(A', I'') → l'
  41. Dilate(D, If[6 < a ≤ 7, 7 - a, 0], H) → D'_1
  42. Vector(D, D'_1) → u
  43. Translate(A', u) → A''
  44. Translate(I'', u) → I'''
  45. Segment(A'', I''') → l''
  46. Segment(H, D) → g_1
  47. Min(g_1, Distance[A, C]) → o
  48. Circle(A, (0.4 * o)) → c_1
  49. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], E) → A'_1
  50. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], G) → A'_2
  51. Dilate(A, If[7 < a ≤ 8, 8 - a, 0], C'_2) → A'_3
  52. Segment(A, A'_1) → h_1
  53. Segment(A, A'_2) → i_1
  54. Segment(A, A'_3) → j_1
  55. Segment(A, E) → k_1
  56. Segment(A, G) → l_1
  57. Intersect(c_1, k_1, 1) → J
  58. Intersect(c_1, l_1, 1) → K
  59. CircleSector(A, K, J) → d_1
  60. Rotate(d_1, If[9 < a ≤ 10, ((-(a - 9)) * ε), (-ε)], A) → e_1
  61. Rotate(e_1, If[11 < a ≤ 12, ((-(a - 11)) * ε), (-ε)], A) → p_1
  62. Dilate(A, If[13 < a ≤ 14, 14 - a, 0], H) → A'_4
  63. Vector(A, A'_4) → v
  64. Translate(p_1, v) → q_1