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Circumcenter/Orthocenter/Centroid

Circumcenter/Orthocenter/Centroid
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2016-10-19 09:24
TriangleCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and relationships of the circumcenter, orthocenter, and centroid of a triangle. Key math concepts include triangle geometry, coordinate geometry, and vector operations. It is constructed using GeoGebra commands/objects like Point, Segment, Circle, Intersect, and Line. Suitable for high school and above students to understand the definitions, properties, and interconnections of these crucial triangle points, laying a foundation for advanced geometric transformations and analytical geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Point(xAxis) → C
  4. Segment(B, A) → f
  5. Segment(C, A) → g
  6. Segment(B, C) → h
  7. Circle(A, 3) → c
  8. Circle(C, 3) → d
  9. Circle(B, 3) → e
  10. Intersect(d, e, 2) → D
  11. Intersect(d, e, 1) → E
  12. Line(D, E) → i
  13. Intersect(c, d, 1) → F
  14. Intersect(c, d, 2) → G
  15. Line(F, G) → j
  16. Intersect(c, e, 1) → H
  17. Intersect(c, e, 2) → I
  18. Line(H, I) → k
  19. Intersect(i, j) → J
  20. Intersect(k, f) → K
  21. Intersect(i, h) → L
  22. Intersect(j, g) → M
  23. Segment(K, C) → l
  24. Segment(M, B) → m
  25. Segment(L, A) → n
  26. Intersect(l, m) → N
  27. Circle(A, P) → p
  28. Intersect(p, h, 1) → Q
  29. Intersect(p, h, 2) → R
  30. Circle(Q, 3) → q
  31. Circle(R, 3) → r
  32. Intersect(q, r, 1) → S
  33. Line(S, A) → s
  34. Circle(E, G) → c_1
  35. Circle(M, 4) → d_1
  36. Circle(A, 1.5) → t
  37. Intersect(t, h, 1) → T
  38. Circle(T, 2) → e_1
  39. Circle(L, 2) → f_1
  40. Intersect(e_1, f_1, 1) → U
  41. Line(A, U) → a
  42. Circle(C, 1) → g_1
  43. Intersect(g_1, xAxis, 2) → W
  44. Segment(C, W) → b
  45. Circle(W, 2) → h_1
  46. Intersect(g_1, h_1, 1) → Z
  47. Circle(Z, 2) → k_1
  48. Intersect(h_1, k_1, 2) → A_1
  49. Line(C, A_1) → i_1
  50. Intersect(a, i_1) → G_1
  51. Intersect(a, i_1) → H_1