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Circumcenter and Circumcircle Demonstration

Circumcenter and Circumcircle Demonstration
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2016-10-17 07:11
TriangleCircleGeometric Construction
This example dynamically demonstrates the construction of the circumcenter and circumcircle of a triangle. Key mathematical concepts involved include circumcenter, circumcircle, perpendicular bisector, midpoint, angle, and line segment. The construction utilizes GeoGebra commands and objects such as Segment, Midpoint, OrthogonalLine, Intersect, Circle, Dilate, Rotate, and more. It is suitable for high school mathematics education to help students understand the fundamental geometric properties and construction methods of triangles.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C_1) → g
  3. Segment(C_1, A) → h
  4. Midpoint(f) → D
  5. Midpoint(h) → E
  6. Midpoint(g) → F
  7. OrthogonalLine(D, f) → i
  8. OrthogonalLine(F, g) → j
  9. OrthogonalLine(E, h) → k
  10. Intersect(k, j) → C
  11. Min(list1) → a
  12. Circle(D, (0.1 * a)) → c
  13. Circle(E, (0.1 * a)) → d
  14. Circle(F, (0.1 * a)) → e
  15. Intersect(c, f, 2) → H
  16. Intersect(c, i) → I, J
  17. Intersect(d, h, 2) → K
  18. Intersect(d, k, 2) → L
  19. Intersect(e, g, 2) → M
  20. Intersect(e, j, 2) → N
  21. CircleSector(D, H, J) → p
  22. CircleSector(F, M, N) → q
  23. CircleSector(E, K, L) → r
  24. Dilate(A, If[0 < b ≤ 1, 1 - b, 0], D) → A'
  25. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], F) → B'
  26. Dilate(C_1, If[4 < b ≤ 5, 5 - b, 0], E) → C'
  27. Segment(A, A') → l
  28. Segment(B, B') → m
  29. Segment(C_1, C') → n
  30. Rotate(A, If[1 < b ≤ 2, ((b - 1) * π), π], D) → A'_1
  31. Rotate(A', If[1 < b ≤ 2, ((b - 1) * π), π], D) → A''
  32. Segment(A'_1, A'') → l'
  33. Rotate(B, If[3 < b ≤ 4, ((b - 3) * π), π], F) → B'_1
  34. Rotate(B', If[3 < b ≤ 4, ((b - 3) * π), π], F) → B''
  35. Segment(B'_1, B'') → m'
  36. Rotate(C_1, If[5 < b ≤ 6, ((b - 5) * π), π], E) → C'_1
  37. Rotate(C', If[5 < b ≤ 6, ((b - 5) * π), π], E) → C''
  38. Segment(C'_1, C'') → n'
  39. Polygon(A, B, C_1) → poly1, c_1, a_1, b_1
  40. Rotate(p, If[6.5 < b ≤ 7.5, ((b - 6.5) * π / 2), π / 2], D) → p'
  41. Rotate(q, If[7.5 < b ≤ 8.5, ((b - 7.5) * π / 2), π / 2], F) → q'
  42. Rotate(r, If[8.5 < b ≤ 9.5, ((b - 8.5) * π / 2), π / 2], E) → r'
  43. Dilate(C, If[10 < b ≤ 11, 11 - b, 0], C_1) → C'_2
  44. Segment(C, C'_2) → s
  45. Angle(C_1, C, A) → α
  46. Angle(A, C, B) → β
  47. Angle(B, C, C_1) → γ
  48. Rotate(C, If[11 < b ≤ 12, ((b - 11) * α), α], C) → C'_3
  49. Rotate(C'_2, If[11 < b ≤ 12, ((b - 11) * α), α], C) → G
  50. Segment(C'_3, G) → s'
  51. Rotate(C'_3, If[12 < b ≤ 13, ((b - 12) * β), β], C) → O
  52. Rotate(G, If[12 < b ≤ 13, ((b - 12) * β), β], C) → G'
  53. Segment(O, G') → s''
  54. Rotate(B, If[13 < b ≤ 14, (((b - 13) * 2) * π), (2 * π)], C) → B'_2
  55. CircleArc(C, B, B'_2) → t
  56. Circle(C, B) → d_1