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Reflection Triangle and Orthocenter

Reflection Triangle and Orthocenter
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2015-02-17 20:58
TriangleCircleVectorGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the triangle A'B'C' formed by reflecting the vertices of triangle ABC across their opposite sides, and the intersections of circles A'BC, B'AC, C'AB. It involves core concepts like reflection transformation, orthocenter, circle intersections, and vector operations. Constructed using GeoGebra commands such as Line, Polygon, Circle, Mirror, Center, Midpoint, Intersect, OrthogonalLine. Suitable for high school mathematics education to explore reflection transformations and geometric properties.

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(A', B, C) → h
  20. Circle(C', A, B) → k
  21. Circle(B', A, C) → p
  22. Intersect(h, k, 2) → H
  23. OrthogonalLine(A, b) → i
  24. OrthogonalLine(C, a) → j
  25. OrthogonalLine(H, c) → l