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Dynamic Demonstration of Circle and Triangle

Dynamic Demonstration of Circle and Triangle
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2016-06-21 19:00
TriangleCircleAngleGeometric ConstructionSlider Animation
This example dynamically demonstrates the relationship between a circle and a triangle. Key mathematical concepts include circles, triangles, angles, and line segments. Using GeoGebra commands such as Circle, PointIn, Tangent, Intersect, etc., a dynamic geometric model is constructed. Suitable for students at the junior high school level and above to learn geometric construction and dynamic geometry concepts.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Distance(A, B) → a
  3. PointIn(b) → C
  4. Tangent(C, c) → d, e
  5. Intersect(c, d) → D
  6. Intersect(c, e) → E
  7. Ray(C, D) → f
  8. Ray(C, E) → g
  9. CircleArc(A, D, E) → h
  10. CircleArc(A, E, D) → k
  11. Point(h) → G
  12. Segment(A, G) → j
  13. CircleArc(A, D, G) → p
  14. Point(p) → F
  15. CircleArc(A, F, G) → q
  16. Segment(A, F) → i
  17. Ray(C, F) → l
  18. Ray(C, G) → m
  19. Intersect(k, m, 1) → H
  20. Intersect(k, l, 1) → I
  21. CircleArc(A, H, I) → r
  22. CircleArc(A, G, H) → s
  23. CircleArc(A, I, F) → t
  24. Angle(F, A, G) → α
  25. Rotate(F, α / 2, A) → F'
  26. Angle(F, A, F') → β
  27. Segment(A, F') → n
  28. Segment(A, I) → a_1
  29. Segment(A, H) → b_1
  30. Angle(H, A, I) → γ
  31. Rotate(H, β / 2, A) → H'
  32. Rotate(H, γ / 2, A) → H'_1
  33. Angle(H, A, H'_1) → δ
  34. Segment(A, H'_1) → c_1
  35. Circle(A, (0.25 * Distance[A, B])) → d_1
  36. Intersect(d_1, j, 1) → J
  37. Intersect(d_1, n, 1) → K
  38. Intersect(d_1, i, 1) → L
  39. Intersect(d_1, a_1, 1) → M
  40. Intersect(d_1, c_1, 1) → N
  41. Intersect(d_1, b_1, 1) → O
  42. CircleSector(A, L, K) → e_1
  43. CircleSector(A, K, J) → f_1
  44. CircleSector(A, O, N) → g_1
  45. CircleSector(A, N, M) → h_1
  46. Angle(N, A, M) → ζ
  47. Point(f) → P
  48. Angle(P, D, A) → η
  49. Point(g) → Q
  50. Angle(A, E, Q) → θ
  51. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], F') → A'
  52. Segment(A, A') → i_1
  53. Angle(F', A, J) → ε
  54. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], H'_1) → A'_1
  55. Segment(A, A'_1) → j_1
  56. Angle(M, A, K) → κ
  57. Rotate(N, κ, A) → N'
  58. Rotate(h_1, If[2.5 < o ≤ 3.5, ((o - 2.5) * κ), κ], A) → k_1
  59. CircleSector(A, L, N') → p_1
  60. Dilate(A, If[4.25 < o ≤ 5.25, 5.25 - o, 0], C) → A'_2
  61. Vector(A, A'_2) → u
  62. Translate(p_1, u) → q_1
  63. Line(A, m) → l_1
  64. Intersect(d_1, c, 1) → R
  65. Intersect(d_1, c) → S, , ,
  66. Intersect(d_1, l_1) → T, U
  67. Angle(N', A, U) → σ
  68. Rotate(q_1, If[5.25 < o ≤ 6.25, ((o - 5.25) * σ), σ], C) → r_1