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Special Points of Triangles

Special Points of Triangles
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2012-11-13 04:35
TriangleCircleAngleGeometric Construction
In collections Besondere Punkte/Special Points Euclidean Geometry
This example demonstrates the dynamic construction of special points in triangles, including the orthocenter and Euler's line. It involves core concepts like angle bisectors, perpendicular bisectors, and intersections. The construction uses commands such as Polygon, LineBisector, Intersect, and Circle. Ideal for high school and above to explore the relationships between these points and Euler's line.

GeoGebra Commands & Parameters

  1. Polygon(H, J, L, Q) → peep, h_2, j_2, l_1, q_1
  2. PointIn(peep) → A
  3. PointIn(peep) → B
  4. PointIn(peep) → C
  5. Polygon(A, B, C) → poli1, c, a, b
  6. LineBisector(c) → d
  7. LineBisector(b) → e
  8. LineBisector(a) → f
  9. Intersect(d, f) → K
  10. Angle(K, M, A) → α
  11. AngularBisector(b, a) → h, i
  12. AngularBisector(b, c) → j, k
  13. AngularBisector(a, c) → l, m
  14. Intersect(i, k) → I
  15. Angle(I, B, A) → γ
  16. Intersect(k, a) → D
  17. OrthogonalLine(I, a) → p
  18. Intersect(a, p) → E
  19. Circle(I, E) → q
  20. OrthogonalLine(C, c) → r
  21. OrthogonalLine(A, a) → s
  22. OrthogonalLine(B, b) → t
  23. Intersect(t, s) → O
  24. Intersect(b, t) → F
  25. Angle(b, t) → δ
  26. Segment(C, M) → a_1
  27. Segment(B, P) → b_1
  28. Segment(A, N) → c_1
  29. Intersect(a_1, c_1) → G
  30. Segment(A, M) → d_1
  31. Segment(M, B) → e_1
  32. Segment(B, N) → f_1
  33. Segment(N, C) → g_1
  34. Segment(C, P) → h_1
  35. Segment(P, A) → i_1
  36. Circle(K, C) → k_1
  37. Line(K, G) → j_1
  38. Angle(C, B, I) → β

AI Drawing Prompt Reference

Draw a triangle and display its angle bisectors, perpendicular bisectors, and the intersections of these lines. Then, find the orthocenter and draw Euler's line. Finally, draw perpendiculars from the vertices to the opposite sides and show the relationships between these perpendiculars and the angle bisectors.
The prompt above was compiled from the original drawing commands and is for reference only.