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Secant Arcs and Angles in Circles

Secant Arcs and Angles in Circles
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2014-05-09 07:02
CircleAngleGeometric Construction
In collections Circles
This example demonstrates how to create secant lines and angles by manipulating points on a circle, illustrating key concepts like the secant theorem and circle angle theorem. It involves constructing circles, lines, intersections, rotations, and measuring angles using GeoGebra commands such as Circle, Line, Intersect, Rotate, CircleArc, and more. Ideal for high school geometry instruction and exploration.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Line(A, a) → b
  3. OrthogonalLine(A, a) → d
  4. Intersect(c, d, 2) → B
  5. Rotate(B, 45*°, A) → B'
  6. Rotate(B, -45*°, A) → B'_1
  7. OrthogonalLine(B', a) → e
  8. OrthogonalLine(B'_1, a) → f
  9. Intersect(c, e, 1) → C
  10. Intersect(c, f, 1) → D
  11. CircleArc(A, B'_1, B') → g
  12. CircleArc(A, C, D) → h
  13. Point(g) → E
  14. Point(h) → F
  15. CircleArc(A, D, B'_1) → k
  16. Point(k) → G
  17. Point(k) → H
  18. Line(E, H) → i
  19. Line(G, F) → j
  20. Intersect(i, j) → I
  21. Segment(I, E) → l
  22. Segment(I, G) → m
  23. Segment(I, H) → n
  24. Segment(I, F) → p
  25. Angle(H, A, G) → α
  26. Angle(E, A, F) → β
  27. Rotate(E, (-α), A) → E'
  28. Angle(H, A, G) → γ
  29. Angle(E, I, F) → δ
  30. CircleArc(A, E, F) → q
  31. CircleArc(A, E', E) → r
  32. CircleArc(A, E, E') → s
  33. CircleSector(A, E, F) → t
  34. Dilate(A, 0.05, E) → A'
  35. Rotate(A', (-α), A) → A''
  36. CircleArc(A, E, E') → c_1
  37. CircleArc(A, E, A'') → d_1
  38. CircleArc(A, A', A'') → e_1
  39. Dilate(A, 0.05, F) → A'_1
  40. Rotate(A'_1, (-δ), A) → L
  41. Rotate(L, (-δ), A) → L'
  42. CircleArc(A, H, G) → f_1
  43. CircleArc(A, G, H) → g_1
  44. Circle(I, Segment[A, A'_1]) → h_1
  45. Intersect(h_1, p, 1) → M
  46. Intersect(h_1, l, 1) → N
  47. CircleArc(I, N, M) → k_1
  48. CircleArc(A, L, F) → p_1
  49. CircleArc(A, L', L) → q_1
  50. Segment(L, A) → a_1
  51. Segment(F, A) → b_1
  52. Segment(L', A) → i_1
  53. Segment(E, A) → j_1
  54. Angle(L', A, L) → ε
  55. Angle(L, A, F) → ζ
  56. Segment(A, F) → l_1