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Isogonal Conjugate of the Nine-Point Center

Isogonal Conjugate of the Nine-Point Center
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2015-02-17 20:53
TriangleCircleGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the construction of the isogonal conjugate of the nine-point center by reflecting the vertices of triangle ABC across the opposite sides. Key mathematical concepts include symmetry, midpoint, segment, polygon, and circle. GeoGebra commands and objects used are Line, Polygon, Circle, Mirror, Center, Midpoint, Segment. Suitable for high school mathematics learning and geometric construction practice.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. Polygon(A, B, C) → poly1, c_1, a_1, b_1
  5. Circle(A, B, C) → s
  6. Mirror(A, b) → A'
  7. Mirror(B, c) → B'
  8. Mirror(C, a) → C'
  9. Line(C', B') → d
  10. Line(B', A') → e
  11. Line(A', C') → f
  12. Polygon(C', B', A') → poly2, a', c', b'
  13. Circle(C', B', A') → g
  14. Center(g) → O'
  15. Center(s) → O
  16. Midpoint(B, C) → D
  17. Midpoint(C, A) → E
  18. Midpoint(A, B) → F
  19. Circle(F, E, D) → h
  20. Center(h) → N
  21. Segment(O', O) → i
  22. Midpoint(i) → N'