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Circumcenter and Circumcircle Construction by Tim Brzezinski

Circumcenter and Circumcircle Construction by Tim Brzezinski
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2016-05-29 08:20
TriangleCircleGeometric Construction
In collections Congruence (CO) Cluster CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems Triangles: Points of Concurrency
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, and Segment, students can understand the properties of the circumcircle. Suitable for middle school and above students to learn 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

AI Drawing Prompt Reference

Draw a triangle ABC and construct its circumcircle. First, use rotation and angle calculations to determine the sides and vertices of the triangle. Then, find the circumcenter, which is the intersection of the perpendicular bisectors of the sides. Next, use the circumcenter and vertices to construct the circumcircle. Finally, apply rotation and scaling operations to ensure the circumcircle passes through all three vertices of the triangle.
The prompt above was compiled from the original drawing commands and is for reference only.