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Circumcenter and Circumcircle Construction

Circumcenter and Circumcircle Construction
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2018-11-12 07:40
TriangleCircleGeometric Construction
This applet dynamically demonstrates the construction of the circumcircle of a triangle. Key concepts include the circumcenter and circumcircle. Using commands like Rotate, Angle, Ray, Segment, students can understand the properties of the circumcircle. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

  1. Rotate(B, (Angle * π / 180), A) → B'
  2. Angle(B, A, B') → α
  3. Ray(A, B') → f
  4. Segment(A, B) → g
  5. Point(f) → C
  6. Polygon(B, A, C) → t1, c, b, a_1
  7. Segment(A, C) → h
  8. Segment(C, B) → i
  9. Midpoint(g) → D
  10. Midpoint(i) → E
  11. Midpoint(h) → F
  12. OrthogonalLine(E, i) → j
  13. OrthogonalLine(D, g) → k
  14. OrthogonalLine(F, h) → l
  15. Intersect(j, k) → G
  16. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], D) → A'
  17. Segment(A, A') → m
  18. Rotate(A, If[1 < d ≤ 2, ((-(d - 1)) * π), (-π)], D) → A'_1
  19. Segment(D, A'_1) → n
  20. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], E) → D'
  21. Segment(B, D') → p
  22. Rotate(B, If[3 < d ≤ 4, ((-(d - 3)) * π), (-π)], E) → B'_1
  23. Segment(E, B'_1) → q
  24. Dilate(C, If[4 < d ≤ 5, 5 - d, 0], F) → C'
  25. Segment(C, C') → r
  26. Rotate(C, If[5 < d ≤ 6, ((-(d - 5)) * π), (-π)], F) → C'_1
  27. Segment(F, C'_1) → s
  28. Dilate(D, If[6 < d ≤ 7, 7 - d, 0], G) → D'_1
  29. Segment(D, D'_1) → t
  30. Angle(G, D, A) → β
  31. Dilate(E, If[7 < d ≤ 8, 8 - d, 0], G) → E'
  32. Segment(E, E') → e
  33. Point(j) → H
  34. Angle(H, E, B) → γ
  35. Dilate(F, If[8 < d ≤ 9, 9 - d, 0], G) → F'
  36. Segment(F, F') → f_1
  37. Angle(G, F, C) → δ
  38. Dilate(G, If[10 < d ≤ 11, 11 - d, 0], C) → G'
  39. Segment(G, G') → g_1
  40. Angle(C, G, A) → ε
  41. Angle(A, G, B) → ζ
  42. Rotate(G, If[11 < d ≤ 12, ((d - 11) * ε), ε], G) → G'_1
  43. Rotate(G', If[11 < d ≤ 12, ((d - 11) * ε), ε], G) → G''
  44. Segment(G'_1, G'') → h_1
  45. CircleArc(G, C, G'') → c_1
  46. Rotate(G'_1, If[12 < d ≤ 13, ((d - 12) * ζ), ζ], G) → I
  47. Rotate(G'', If[12 < d ≤ 13, ((d - 12) * ζ), ζ], G) → G'''
  48. Segment(I, G''') → i_1
  49. CircleArc(G, A, G''') → d_1
  50. Rotate(I, If[13 < d ≤ 14, ((d - 13) * ((2 * π) - ε - ζ)), (2 * π) - ε - ζ], G) → I'
  51. Rotate(G''', If[13 < d ≤ 14, ((d - 13) * ((2 * π) - ε - ζ)), (2 * π) - ε - ζ], G) → J
  52. Segment(I', J) → j_1
  53. CircleArc(G, B, J) → e_1
  54. Segment(A, D) → a
  55. Segment(D, B) → k_1
  56. Segment(B, E) → l_1
  57. Segment(E, C) → m_1
  58. Segment(C, F) → n_1
  59. Segment(F, A) → p_1