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Animation 28: Circumcircle and Geometric Constructions

Animation 28: Circumcircle and Geometric Constructions
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2016-06-16 10:11
CircleGeometric Construction
This example demonstrates the construction of a circumcircle through animation, illustrating its relationship with triangles. Key math concepts include circumcircle, geometric construction, rotation, and dilation. GeoGebra commands like Segment, Midpoint, OrthogonalLine, Intersect, Circle, Rotate, and Dilate are used in the construction. Suitable for high school mathematics education to understand geometric transformations and properties.

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