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Circumcenter of Reflection Triangle

Circumcenter of Reflection Triangle
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2015-02-16 09:37
TriangleCircleTransformationGeometric Construction
In collections Reflections in Triangle Geometry
This example demonstrates that the isogonal conjugate point P* of point P is the circumcenter of the reflection triangle generated by P. Key concepts include isogonal conjugation, reflection triangle, and circumcenter. Constructed using GeoGebra commands such as Polygon, Mirror, Segment, etc. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Mirror(P, b) → P'
  3. Mirror(P, c) → P'_1
  4. Mirror(P, a) → P'_2
  5. Segment(P'_1, P'_2) → d
  6. Segment(P'_2, P') → e
  7. Segment(P', P'_1) → f
  8. Segment(P, P') → g
  9. Segment(P'_1, P) → h
  10. Segment(P, P'_2) → i
  11. AngularBisector(B, A, C) → j
  12. AngularBisector(C, B, A) → k
  13. Line(A, P) → l
  14. Line(B, P) → m
  15. Mirror(l, j) → l'
  16. Mirror(m, k) → m'
  17. Intersect(l', m') → D
  18. Line(A, P) → n
  19. Mirror(n, j) → n'
  20. Point(n') → E
  21. Segment(E, P'_1) → p
  22. Segment(E, P') → q
  23. Circle(D, P') → r