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Dynamic Relationship of Triangle and Circumcenter

Dynamic Relationship of Triangle and Circumcenter
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2017-10-10 05:12
TriangleCircleGeometric ConstructionSlider AnimationLocus
This example dynamically illustrates the relationship involving any triangle, one of its cevians, the circumcenter of the original triangle, and the circumcircle. It covers core math concepts like circumcircle, triangles, medians, angles, congruence, and curve sketching. Construction uses commands such as Rotate, Angle, Segment, Ray, Point, Min, Circle, Intersect, CircleSector, Polygon, LineBisector, and Dilate. Suitable for high school mathematics education to understand geometric properties and dynamic variations of triangles and circumcenters.

GeoGebra Commands & Parameters

  1. Rotate(A, (a * π / 180), B) → A'
  2. Angle(A, B, A') → α
  3. Segment(B, A) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(B, C) → h
  7. Segment(C, A) → i
  8. Min(f, h) → b
  9. Circle(B, (0.2 * b)) → c
  10. Intersect(c, f, 1) → D
  11. Intersect(c, h, 1) → E
  12. CircleSector(B, D, E) → d
  13. Polygon(B, A, C) → t1, c_1, b_1, a_1
  14. Point(f) → F
  15. Segment(C, F) → j
  16. LineBisector(C, F) → k
  17. LineBisector(F, B) → l
  18. Intersect(l, k) → G
  19. LineBisector(F, A) → m
  20. Intersect(k, m) → H
  21. LineBisector(C, A) → n
  22. LineBisector(A, B) → p
  23. Intersect(p, n) → I
  24. LineBisector(C, H) → q
  25. LineBisector(H, I) → r
  26. Intersect(q, r) → J
  27. Circle(J, I) → e
  28. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], F) → C'
  29. Segment(C, C') → s
  30. Polygon(B, F, C) → t2, c_2, b_2, f_1
  31. Polygon(F, A, C) → t3, c_3, f_2, a_2
  32. Dilate(G, If[2 < o < 3, 3 - o, 0], C) → G'
  33. Segment(G, G') → t
  34. Circle(G, G') → d_1
  35. Dilate(H, If[4 < o < 5, 5 - o, 0], A) → H'
  36. Segment(H, H') → g_1
  37. Circle(H, H') → e_1
  38. Dilate(I, If[7 < o < 8, 8 - o, 0], A) → I'
  39. Segment(I, I') → h_1
  40. Circle(I, I') → k_1
  41. Dilate(J, If[10.5 < o < 11.5, 11.5 - o, 0], I) → J'
  42. Segment(J, J') → i_1
  43. Circle(J, J') → p_1