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Ellipse and Orthocenter Locus Problem

Ellipse and Orthocenter Locus Problem
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2016-10-12 08:27
Geometric ConstructionLocus
In collections Locus Constructions
This example demonstrates the geometric relationship between an ellipse and the locus of its orthocenter. Core math concepts include ellipse, orthocenter, geometric construction, intersection, and circle. Construction highlights involve commands/objects like Circle, Segment, PointIn, Point, LineBisector, Midpoint, Line, Intersect, and Ellipse in GeoGebra. Suitable for high school mathematics teaching or exploration by geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(O, R) → c
  2. Segment(O, R) → f
  3. PointIn(a) → A
  4. Point(c) → D
  5. LineBisector(A, D) → g
  6. Midpoint(O, A) → E
  7. Segment(O, R) → h
  8. Line(A, O) → k
  9. Segment(O, D) → i
  10. Intersect(g, i) → F
  11. Segment(A, F) → j
  12. Segment(F, O) → l
  13. Circle(E, b / 2) → d
  14. Intersect(d, k, 1) → G
  15. Intersect(d, k, 2) → H
  16. Ellipse(A, O, H) → e