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In-centre, Circumcentre, Centroid and Orthocentre

In-centre, Circumcentre, Centroid and Orthocentre
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2014-11-29 23:50
TriangleCoordinate GeometryGeometric Construction
In collections GCSE Higher Ch8 Transformations & Constructions
This example demonstrates the in-centre, circumcentre, centroid, and orthocentre of a triangle. These points are the intersection of the angle bisectors, the center of the circumcircle, the intersection of the medians, and the intersection of the altitudes, respectively. Using GeoGebra commands such as Polygon, AngularBisector, and Intersect, the geometric concepts are visually illustrated. Suitable for students at the middle school level and above to learn about triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. AngularBisector(c, a) → d, e
  3. AngularBisector(c, b) → f, g
  4. AngularBisector(a, b) → h, i
  5. Intersect(e, g) → D
  6. OrthogonalLine(D, a) → k
  7. Intersect(k, a) → E
  8. Circle(D, E) → p
  9. Segment(D, E) → l
  10. Segment(E, C) → m
  11. Angle(C, E, D) → α
  12. LineBisector(a) → q
  13. LineBisector(c) → r
  14. LineBisector(b) → s
  15. Intersect(q, r) → F
  16. Intersect(r, c) → G
  17. Intersect(s, b) → H
  18. Intersect(q, a) → I
  19. Segment(B, G) → t
  20. Segment(G, A) → a_1
  21. Angle(c, r) → β
  22. Circle(F, B) → c_1
  23. Segment(A, H) → b_1
  24. Segment(H, C) → d_1
  25. Segment(B, I) → e_1
  26. Segment(I, C) → f_1
  27. Angle(f_1, q) → γ
  28. Angle(s, b_1) → δ
  29. OrthogonalLine(A, a) → g_1
  30. OrthogonalLine(B, b) → h_1
  31. OrthogonalLine(C, c) → i_1
  32. Intersect(g_1, h_1) → J
  33. Line(B, C) → j_1
  34. Line(B, A) → k_1
  35. Line(A, C) → l_1
  36. Intersect(g_1, j_1) → K
  37. Intersect(h_1, l_1) → L
  38. Intersect(i_1, k_1) → M
  39. Angle(i_1, k_1) → ε
  40. Angle(j_1, g_1) → ζ
  41. Midpoint(A, K) → N
  42. Midpoint(B, L) → O
  43. Midpoint(C, M) → P
  44. Angle(h_1, l_1) → η
  45. Midpoint(t) → Q
  46. Midpoint(c) → R
  47. Midpoint(b) → S
  48. Midpoint(a) → T
  49. Segment(A, T) → m_1
  50. Segment(B, S) → n_1
  51. Segment(C, R) → p_1
  52. Intersect(m_1, n_1) → U
  53. Line(F, J) → q_1

AI Drawing Prompt Reference

Draw a triangle and its angle bisectors, altitudes, medians, and perpendicular bisectors, labeling their intersections as incenter, circumcenter, centroid, and orthocenter. Also, draw the circumcircle and incircle, and label relevant segments and angles to illustrate the relationships between these geometric concepts.
The prompt above was compiled from the original drawing commands and is for reference only.