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Chord Properties

Chord Properties
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2017-12-22 21:50
TriangleCircleGeometric Construction
In collections Mathematics Form 2
This example demonstrates the properties of a chord in a circle, including relationships between the chord, the center of the circle, the perpendicular bisector, and inscribed angles. Core mathematical concepts involve circles, similar triangles, the inscribed angle theorem, and the chord bisector theorem. The construction utilizes GeoGebra commands such as Circle, Point, Segment, Intersect, OrthogonalLine, Angle, If, CircleArc, Line, Semicircle, Rotate, DynamicCoordinates, Distance, Length, and LineBisector. It is suitable for high school students and educators exploring circle properties, geometric constructions, and dynamic geometry.

GeoGebra Commands & Parameters

  1. SelectedIndex(Bahasa) → nn
  2. Circle(O, Rd) → c
  3. Point(c) → D
  4. Point(c) → B
  5. Point(c) → A
  6. Segment(A, B) → g
  7. Circle(D, g) → e
  8. Intersect(c, e, 1) → J
  9. Segment(D, J) → n
  10. OrthogonalLine(O, n) → q
  11. Intersect(q, n) → L
  12. OrthogonalLine(O, g) → i
  13. Intersect(i, g) → K
  14. Angle(K, O, L) → γ
  15. Angle(A, O, B) → α
  16. If(α ≤ 180°, A, B) → M
  17. If(α ≤ 180°, B, A) → N
  18. If(γ > 180°, Rotate[N, ((-a) * (360° - γ)), O], Rotate[N, (a * γ), O]) → S
  19. If(γ > 180°, Rotate[M, ((-a) * (360° - γ)), O], Rotate[M, (a * γ), O]) → R
  20. CircleArc(O, M, N) → Arc1
  21. Point(Arc1) → G
  22. Intersect(Arc1, i) → F, E_1
  23. Line(O, A) → f
  24. Intersect(c, f, 2) → P
  25. Semicircle(A, P) → d
  26. Rotate(d, ((a * 180))°, O) → d'
  27. If(Distance[G, F] < 0.2, F, G) → T
  28. If(nn ≟ 1, {"Properties of diameter", "Properties of chord 1", "Properties of chord 2", "Properties of chord 3", "Properties of chord 4"}, {"Sifat diameter", "Sifat perentas 1", "Sifat perentas 2", "Sifat perentas 3", "Sifat perentas 4"}) → Sifat
  29. SelectedIndex(Sifat) → m
  30. DynamicCoordinates(G, x(T), y(T)) → C
  31. Line(C, O) → h
  32. Intersect(h, g) → E
  33. If(α > 180°, Rotate[B, (((-a) * 180))°, E], Rotate[B, ((a * 180))°, E]) → B'
  34. Segment(E, B') → j
  35. Angle(A, E, O) → β
  36. CircleArc(O, R, S) → p
  37. Segment(C, O) → l
  38. If(γ > 180°, Rotate[K, ((-u) * (360° - γ)), O], Rotate[K, (u * γ), O]) → W
  39. Segment(O, W) → t
  40. Segment(R, S) → f_1
  41. Angle(O, K, B) → ε
  42. Angle(O, L, D) → ζ
  43. If(γ > 180°, Rotate[M, (-(360° - γ)), O], Rotate[M, γ, O]) → U
  44. If(γ > 180°, Rotate[N, (-(360° - γ)), O], Rotate[N, γ, O]) → V
  45. CircleArc(O, U, V) → Arc2
  46. Distance(R, S) → RS
  47. Length(p) → PL
  48. Distance(O, W) → OW
  49. Point(c) → Z
  50. Segment(D, Z) → b
  51. LineBisector(D, Z) → g_1
  52. LineBisector(B, A) → h_1
  53. Intersect(g_1, b) → A_1
  54. Intersect(h_1, g) → B_1
  55. Angle(O, A_1, D) → η
  56. Angle(O, B_1, A) → θ
  57. Segment(A, P) → k