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Special Points in a Triangle by Zoltán Kovács

Special Points in a Triangle by Zoltán Kovács
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2015-10-22 05:27
TriangleVectorCoordinate Geometry
In collections Besondere Punkte/Special Points
This example demonstrates special points in a triangle, including altitudes, orthocenter, medians, and circumcenter. It involves the geometric properties and construction methods of triangles. Using GeoGebra commands such as Polygon, OrthogonalLine, and Intersect, it provides a visual understanding of these concepts. Suitable for middle and high school students studying triangle geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. OrthogonalLine(A, a) → h_A
  3. OrthogonalLine(B, b) → h_B
  4. OrthogonalLine(C, c) → h_C
  5. Intersect(h_A, h_B) → H
  6. Midpoint(a) → D
  7. Midpoint(b) → E
  8. Midpoint(c) → F
  9. Segment(A, D) → e
  10. Segment(B, E) → f_1
  11. Segment(C, F) → g
  12. Intersect(e, f_1) → S
  13. LineBisector(a) → h
  14. LineBisector(b) → i
  15. LineBisector(c) → j
  16. Intersect(i, h) → U
  17. Line(S, H) → l
  18. Midpoint(A, H) → A'
  19. Midpoint(B, H) → B'
  20. Midpoint(H, C) → C'
  21. Intersect(h_A, a) → F_A
  22. Intersect(h_B, b) → F_B
  23. Intersect(h_C, c) → F_C
  24. Circle(A', F, F_C) → k_F

AI Drawing Prompt Reference

Draw a triangle ABC, then draw its three altitudes, which intersect at the orthocenter H. Next, draw the three medians, which intersect at the centroid S. Then, draw the circumcircle of the triangle. Finally, draw the three angle bisectors, which intersect at the incenter U.
The prompt above was compiled from the original drawing commands and is for reference only.