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Circumcenter and Circumcircle of a Triangle

Circumcenter and Circumcircle of a Triangle
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2017-06-13 04:08
TriangleCircleGeometric Construction
This applet dynamically demonstrates the construction of the circumcircle of a triangle. Key concepts include the circumcenter and circumcircle. Using GeoGebra commands such as Segment, Midpoint, OrthogonalLine, etc., the construction process is clearly illustrated. Suitable for students in middle school and above to learn geometric construction and related concepts.

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