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The Fermat Point and the Kiepert Hyperbola

The Fermat Point and the Kiepert Hyperbola
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2017-06-04 19:55
TriangleAngleTransformationLocus
This example demonstrates the geometric relationship and properties between the Fermat Point and the Kiepert Hyperbola. Key math concepts include triangles, angles, rotations, geometric transformations, and loci. Construction involves commands like Segment, Line, Rotate, Intersect, Polygon, Angle, and Locus in GeoGebra. Suitable for high school and above students to understand dynamic relationships between geometric transformations and loci.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Line(A, B) → i
  5. Line(B, C) → j
  6. Line(C, A) → k
  7. Rotate(i, α, A) → i'
  8. Rotate(i, (-α), B) → i'_1
  9. Intersect(i', i'_1) → C'
  10. Rotate(k, (-α), A) → k'
  11. Rotate(k, α, C) → k'_1
  12. Intersect(k', k'_1) → B'
  13. Rotate(j, α, B) → j'
  14. Rotate(j, (-α), C) → j'_1
  15. Intersect(j', j'_1) → A'
  16. Polygon(C, B', A) → poly1, a, c, e
  17. Polygon(A, C', B) → poly2, b, a_1, d
  18. Polygon(C, A', B) → poly3, b_1, c_1, f_1
  19. Angle(A, C, B') → β
  20. Angle(B', A, C) → γ
  21. Angle(B, A, C') → δ
  22. Angle(C', B, A) → ε
  23. Angle(A', C, B) → ζ
  24. Angle(C, B, A') → η
  25. Line(C, C') → l
  26. Line(B', B) → m
  27. Line(A', A) → n
  28. Intersect(l, m) → F
  29. Locus(F, α) → loc1