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Inscribed Angles Discovery

Inscribed Angles Discovery
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2016-06-03 08:39
CircleAngleTrigonometryGeometric ConstructionSlider Animation
In collections Circles (Theorems)
This example demonstrates the inscribed angle theorem geometrically by dynamically showing the relationship between central and inscribed angles in a circle. It involves core concepts like circle, angle, intersection, tangent line, rotation, similarity, etc. Construction highlights GeoGebra commands: Circle, Point, CircleArc, Segment, Angle, Rotate, Intersect, CircleSector, Dilate, Vector, Line, Translate. Suitable for high school geometry teaching to enhance understanding of the inscribed angle theorem.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. CircleArc(A, D, C) → d
  5. Point(d) → E
  6. Point(d) → F
  7. CircleArc(A, C, D) → e
  8. Segment(A, C) → a
  9. Segment(A, D) → b
  10. Segment(E, C) → f
  11. Segment(E, D) → g
  12. Segment(F, C) → h
  13. Segment(F, D) → i
  14. Angle(C, A, D) → α
  15. Rotate(C, α / 2, A) → C'
  16. Angle(C, A, C') → β
  17. Segment(A, C') → j
  18. Circle(E, (0.25 * Distance[A, B])) → k
  19. Intersect(k, f, 1) → G
  20. Intersect(k, g, 1) → H
  21. Circle(F, (0.25 * Distance[A, B])) → p
  22. Intersect(p, h, 1) → J
  23. Intersect(p, i, 1) → K
  24. CircleSector(E, G, H) → q
  25. CircleSector(F, J, K) → r
  26. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], A) → E'
  27. Vector(E, E') → u
  28. Line(E, a) → m
  29. Intersect(k, m, 2) → L
  30. Angle(L, E, G) → γ
  31. Dilate(E, If[2 < l ≤ 3, 3 - l, 0], A) → E'_1
  32. Vector(E, E'_1) → v
  33. Line(E, j) → n
  34. Intersect(k, n, 2) → M
  35. Angle(M, E, G) → δ
  36. Circle(A, (0.25 * Distance[A, B])) → t
  37. Intersect(t, a, 1) → N
  38. Intersect(t, j, 1) → O
  39. Intersect(t, c, 1) → I
  40. Intersect(t, b) → P,
  41. CircleArc(A, N, P) → c_1
  42. Point(d) → Q
  43. Segment(Q, C) → a_1
  44. Segment(Q, D) → b_1
  45. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], F) → E'_2
  46. Dilate(E, If[0 < l ≤ 1, 1 - l, 0], Q) → E'_3
  47. Vector(E, E'_2) → w
  48. Vector(E, E'_3) → s
  49. Translate(q, w) → q'
  50. Translate(q, s) → q'_1
  51. Line(E, i) → d_1
  52. Intersect(k, d_1) → R, S
  53. Angle(H, E, S) → ε
  54. Rotate(q', ((l - 1) * ε), F) → q''
  55. Line(E, a_1) → e_1
  56. Intersect(k, e_1) → T, U
  57. Angle(U, E, G) → ζ
  58. Rotate(q'_1, ((-(l - 1)) * ζ), Q) → f_1
  59. Segment(C, D) → g_1