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Locus of the Orthocenter

Locus of the Orthocenter
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2015-03-24 00:20
TriangleCircleGeometric ConstructionLocus
This example demonstrates the path traced by the orthocenter G of a triangle as vertex A moves along a circular arc. Key math concepts include orthocenter, locus, and geometric transformations. Constructed using GeoGebra commands like Circle, Point, Segment, OrthogonalLine, Intersect, and Angle, with a Slider for animation. Suitable for high school geometry education to explore orthocenter properties and locus relationships.

GeoGebra Commands & Parameters

  1. Circle(L, T) → c
  2. Point(c) → A
  3. Point(c) → B
  4. Point(c) → C
  5. Segment(A, C) → a
  6. Segment(C, B) → b
  7. Segment(B, A) → d
  8. OrthogonalLine(A, b) → e
  9. OrthogonalLine(C, d) → f
  10. OrthogonalLine(B, a) → g
  11. Intersect(g, a) → D
  12. Intersect(d, f) → E
  13. Intersect(e, b) → F
  14. Intersect(e, f) → G
  15. Segment(A, F) → h
  16. Segment(B, D) → i
  17. Segment(C, E) → j
  18. Angle(C, F, A) → α
  19. Angle(B, E, C) → β
  20. Angle(A, D, B) → γ

AI Drawing Prompt Reference

Draw a triangle ABC with vertex A moving along a circular arc. Construct the altitudes of the triangle, and the intersection point G is the orthocenter. Observe the path traced by the orthocenter G as A moves.
The prompt above was compiled from the original drawing commands and is for reference only.