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Concurrent Points Demo

Concurrent Points Demo
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2019-01-10 09:14
TriangleGeometric Construction
This example demonstrates the concurrency of medians, angle bisectors, and altitudes in a triangle, highlighting the centroid, circumcenter, and incenter. It involves core concepts like triangle centers, angle bisectors, medians, altitudes, and geometric properties. Constructed using commands like Polygon, Angle, LineBisector, Intersect, Segment, AngularBisector, OrthogonalLine, Midpoint, Line. Suitable for high school geometry education and exploration of geometric properties.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Angle(B, A, C) → α
  3. Angle(A, B, C) → β
  4. Angle(A, C, B) → γ
  5. LineBisector(c) → f
  6. LineBisector(a) → g
  7. LineBisector(b) → h
  8. Intersect(g, a) → D
  9. Intersect(h, b) → E
  10. Intersect(f, c) → F
  11. Intersect(f, g) → Circumcenter
  12. Segment(Circumcenter, F) → i
  13. Segment(Circumcenter, D) → j
  14. Segment(Circumcenter, E) → k
  15. AngularBisector(B, A, C) → l
  16. AngularBisector(B, C, A) → m
  17. AngularBisector(A, B, C) → n
  18. Intersect(l, m) → Incenter
  19. Segment(A, Incenter) → p
  20. Segment(B, Incenter) → q
  21. Segment(C, Incenter) → r
  22. Segment(Circumcenter, B) → s
  23. Segment(Circumcenter, C) → t
  24. Segment(Circumcenter, A) → f_1
  25. OrthogonalLine(Incenter, b) → g_1
  26. OrthogonalLine(Incenter, c) → h_1
  27. OrthogonalLine(Incenter, a) → i_1
  28. Intersect(i_1, a) → I
  29. Intersect(g_1, b) → J
  30. Intersect(h_1, c) → K
  31. Segment(Incenter, K) → j_1
  32. Segment(Incenter, I) → k_1
  33. Segment(Incenter, J) → l_1
  34. Midpoint(a) → L
  35. Midpoint(b) → M
  36. Midpoint(c) → N
  37. Segment(A, L) → m_1
  38. Segment(B, M) → n_1
  39. Segment(C, N) → p_1
  40. Intersect(m_1, n_1) → Centroid
  41. Segment(A, Centroid) → q_1
  42. Segment(Centroid, L) → r_1
  43. Segment(N, Centroid) → s_1
  44. Segment(Centroid, C) → t_1
  45. Segment(M, Centroid) → a_1
  46. Segment(Centroid, B) → b_1
  47. OrthogonalLine(C, c) → c_1
  48. OrthogonalLine(A, a) → d_1
  49. OrthogonalLine(B, b) → e_1
  50. Line(A, C) → i_2
  51. Line(C, B) → j_2
  52. Line(A, B) → k_2
  53. OrthogonalLine(A, j_2) → f_2
  54. OrthogonalLine(B, i_2) → g_2
  55. OrthogonalLine(C, k_2) → h_2
  56. Intersect(f_2, g_2) → Orthocenter
  57. Intersect(k_2, h_2) → Q
  58. Intersect(j_2, f_2) → R
  59. Intersect(i_2, g_2) → S
  60. Segment(B, S) → l_2
  61. Segment(C, Q) → m_2
  62. Segment(A, R) → n_2
  63. Segment(Orthocenter, Q) → p_2
  64. Segment(Orthocenter, R) → q_2
  65. Segment(Orthocenter, S) → r_2