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Triangle Centers

Triangle Centers
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2015-02-25 11:41
TriangleCoordinate GeometryGeometric Construction
This example demonstrates eight centers of a triangle, including the centroid and orthocenter. Using GeoGebra commands such as Polygon, LineBisector, and Circle, the geometric significance of these centers can be visually understood. Suitable for students at the junior high school level and above to learn about the geometric properties of triangles.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → d
  3. OrthogonalLine(C, c) → e
  4. OrthogonalLine(B, b) → f
  5. Intersect(d, f) → C_1
  6. LineBisector(b) → h
  7. LineBisector(c) → i
  8. LineBisector(a) → j
  9. Intersect(j, h) → C_2
  10. Circle(C_2, C) → k
  11. AngularBisector(C, B, A) → m
  12. AngularBisector(B, A, C) → n
  13. AngularBisector(A, C, B) → p
  14. Intersect(n, m) → C_3
  15. OrthogonalLine(C_3, a) → q
  16. Intersect(q, a) → G
  17. Circle(C_3, G) → r
  18. Midpoint(b) → H
  19. Midpoint(c) → I
  20. Midpoint(a) → J
  21. Segment(A, J) → s
  22. Segment(C, I) → t
  23. Segment(B, H) → a_1
  24. Intersect(a_1, t) → C_4
  25. Segment(C_2, C_1) → b_1
  26. Line(C, B) → bc
  27. Line(C, A) → ac
  28. Line(A, B) → ab
  29. Intersect(d, bc) → L
  30. Intersect(f, ac) → M
  31. Intersect(ab, e) → N
  32. Segment(A, L) → f_1
  33. Segment(C, N) → g_1
  34. Segment(B, M) → h_1
  35. Polygon(C, B, 3) → poly2, i_1, j_1, k_1, O
  36. Polygon(A, C, 3) → poly3, l_1, m_1, n_1, P
  37. Polygon(B, A, 3) → poly4, p_1, q_1, r_1, Q
  38. Polygon(A, B, 3) → poly5, b_2, c_2, d_2, S
  39. Polygon(B, C, 3) → poly6, e_2, f_2, g_2, T
  40. Polygon(C, A, 3) → poly7, h_2, i_2, j_2, U
  41. Circle(S, B, A) → c_1
  42. Circle(B, T, C) → d_1
  43. Circle(U, A, C) → e_1
  44. LineBisector(r_1) → p_2
  45. LineBisector(q_1) → q_2
  46. Intersect(p_2, q_2) → R
  47. Line(C, R) → s_1
  48. LineBisector(m_1) → t_1
  49. LineBisector(n_1) → a_2
  50. Intersect(t_1, a_2) → A_1
  51. Line(B, A_1) → n_2
  52. LineBisector(k_1) → r_2
  53. LineBisector(j_1) → s_2
  54. Intersect(r_2, s_2) → B_1
  55. Line(A, B_1) → t_2
  56. Intersect(t_2, n_2) → C_7
  57. Circle(B, A, Q) → c_3
  58. Circle(C, A, P) → d_3
  59. Circle(C, B, O) → e_3
  60. Intersect(c_3, e_3) → D_1, C_8, ,
  61. Intersect(c_1, d_1, 2) → C_6
  62. Center(c_1) → W
  63. Center(d_1) → Z
  64. Center(e_1) → F_1
  65. Segment(F_1, B) → k_2
  66. Segment(W, C) → l_2
  67. Segment(A, Z) → m_2
  68. Intersect(m_2, k_2) → C_5
  69. Segment(P_1, P_2) → b_3
  70. Segment(P_2, P_6) → f_3
  71. Line(P_1, P_2) → a_3
  72. Line(P_2, P_8) → g_3
  73. Line(P_2, P_6) → h_3

AI Drawing Prompt Reference

Draw a triangle ABC, then sequentially draw its circumcenter, orthocenter, incenter, centroid, nine-point circle center, Euler line, incircle center, and excircle centers, and label the relationships between these centers.
The prompt above was compiled from the original drawing commands and is for reference only.