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Isogonal Conjugates: Orthocenter, Circumcenter, Incenter

Isogonal Conjugates: Orthocenter, Circumcenter, Incenter
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2019-08-04 05:21
TriangleAngleGeometric Construction
This example illustrates the isogonal conjugate property, particularly the isogonal conjugates of the orthocenter, circumcenter, and incenter of a triangle. Key mathematical concepts include the orthocenter, circumcenter, and incenter of a triangle. Using GeoGebra commands such as Line, Polygon, AngularBisector, Mirror, Intersect, etc., these special points can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. Polygon(A, B, C) → t1, c, a, b
  5. Line(A, P) → i
  6. Line(B, P) → j
  7. Line(P, C) → k
  8. AngularBisector(B, A, C) → l
  9. AngularBisector(A, C, B) → m
  10. AngularBisector(C, B, A) → n
  11. Mirror(i, l) → i'
  12. Mirror(j, n) → j'
  13. Mirror(k, m) → k'
  14. Intersect(i', j') → P'
  15. Intersect(l, m) → I
  16. OrthogonalLine(A, g) → p
  17. OrthogonalLine(B, h) → q
  18. Intersect(p, q) → H
  19. Center(Circle[A, B, C]) → O

AI Drawing Prompt Reference

Draw a triangle and its orthocenter, circumcenter, and incenter. Then, construct the three angle bisectors of the triangle, reflect the altitudes over these bisectors, and find the intersections of the reflected lines. Finally, connect the orthocenter and circumcenter, and find their intersection to locate the incenter.
The prompt above was compiled from the original drawing commands and is for reference only.