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Circumcircle Exploration of a Triangle

Circumcircle Exploration of a Triangle
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2016-10-29 02:43
TriangleCircleGeometric Construction
This applet dynamically demonstrates the construction of the circumcircle of a triangle. Key concepts include the circumcenter and properties of the circumcircle. Using GeoGebra commands such as Segment, Midpoint, and OrthogonalLine, students can understand the basics of geometric construction. Suitable for middle school and above students to learn about geometric construction and circles.

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

AI Drawing Prompt Reference

Draw a triangle ABC, then construct its circumcircle. First, connect each pair of triangle vertices to form three line segments. Find the midpoints of these segments, draw perpendicular lines from these midpoints to the opposite sides, and find their intersection point O, which is the circumcenter. Use O as the center and the length of OA as the radius to draw the circumcircle.
The prompt above was compiled from the original drawing commands and is for reference only.