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Orthocenter and Circumcenter as Isogonal Conjugates

Orthocenter and Circumcenter as Isogonal Conjugates
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2018-03-21 06:31
TriangleCircleGeometric Construction
This example demonstrates the relationship between the orthocenter and circumcenter of a triangle as isogonal conjugates. Key mathematical concepts include orthocenter, circumcenter, isogonal conjugate, and triangle geometry. Construction highlights the use of GeoGebra commands and objects such as Line, OrthogonalLine, Intersect, Mirror, Circle, and LineBisector. Suitable for high school and above students to understand special points in triangles and geometric construction techniques.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. OrthogonalLine(A, g) → i
  5. OrthogonalLine(B, h) → j
  6. OrthogonalLine(C, f) → k
  7. Intersect(i, j) → D
  8. Mirror(D, f) → D'
  9. Mirror(D, g) → D'_1
  10. Mirror(D, h) → D'_2
  11. Circle(D'_1, D', D'_2) → c
  12. LineBisector(C, B) → l
  13. LineBisector(B, A) → m
  14. LineBisector(A, C) → n
  15. Intersect(l, m) → E