Trisecting a Semicircle and Diameter

Trisecting a Semicircle and Diameter
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2026-04-27 05:40
This example demonstrates how to trisect a semicircle and its diameter simultaneously. It involves basic geometric concepts, including angles, circles, and lines. Using GeoGebra commands, users can easily create this graph and explore its properties. Suitable for middle school or high school students learning geometry and circle properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → C
  2. Point(xAxis) → A
  3. Polygon(C, A, 3) → polígono1, f, g, h, B
  4. Ray(C, D) → i
  5. Ray(C, E) → j
  6. Semicircle(B, A) → c
  7. Intersect(c, i, 1) → F
  8. Intersect(c, j, 1) → G
  9. Center(c) → M
  10. Angle(G, M, B) → α
  11. Angle(G, M, F) → β
  12. Angle(A, M, F) → γ
  13. Circle(M, B) → d
  14. Segment(M, G) → k
  15. Segment(M, F) → l
  16. Segment(C, G) → m
  17. Segment(C, F) → n
  18. Segment(B, E) → b
  19. Segment(E, D) → q
  20. Segment(D, A) → r
  21. Mirror(G, E) → G'
  22. Mirror(E, G') → E'
  23. Segment(B, G) → p
  24. Angle(C, B, A) → δ
  25. Angle(A, B, G) → ε
  26. Segment(B, F) → s
  27. Segment(F, A) → t
  28. Angle(B, F, A) → ζ
  29. Angle(C, B, F) → η
  30. Angle(F, A, D) → θ
  31. Angle(D, A, C) → ι
  32. ClosestPoint(f, B) → H
  33. Segment(B, H) → f_1
  34. Segment(G, A) → h_1
  35. Angle(A, H, B) → κ
  36. Angle(G, A, H) → λ
  37. ClosestPoint(f, E) → K
  38. Segment(E, K) → i_1
  39. Angle(A, K, E) → μ
  40. ClosestPoint(h_1, E) → L
  41. Segment(E, L) → g_1
  42. Angle(E, L, A) → ν
  43. Angle(B, G, A) → ξ
  44. Mirror(C, q) → C'
  45. Segment(B, C') → j_1
  46. Segment(C', A) → k_1
  47. Segment(G, F) → l_1
  48. Segment(A_1, T) → m_1
  49. Segment(B_1, S) → n_1
  50. Segment(C_1, M) → p_1
  51. Segment(D_1, R) → q_1
  52. Segment(E_1, Q) → r_1
  53. Segment(J, W) → t_1
  54. Segment(I, Z) → s_1
  55. Segment(N, M) → a_1
  56. Segment(O, V) → b_1
  57. Segment(P, U) → c_1

AI Drawing Prompt Reference

Draw a semicircle and its diameter, trisecting both simultaneously. Start by marking the intersection of the coordinate axes and a point on the semicircle, then form a triangle. Draw two rays from the intersection point, and a semicircle with the point on the semicircle as the center. Find the intersections of the rays with the semicircle. Calculate angles, draw circles and segments connecting key points. Finally, mirror parts of the figure to complete the trisection construction.
The prompt above was compiled from the original drawing commands and is for reference only.