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Steiner Circum- and In- Ellipse

Steiner Circum- and In- Ellipse
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2019-04-28 18:11
Coordinate Geometry
This example demonstrates Steiner circum- and in- ellipses. Key mathematical concepts include ellipse, rectangle, means, perimeter, and quadratic equations. Using GeoGebra commands such as Intersect, Segment, Conic, Center, etc., these ellipses can be constructed. Suitable for high school mathematics education, particularly in the study of coordinate geometry and ellipses.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → B
  2. Segment(A, B) → AB
  3. Segment(B, C) → BC
  4. Segment(C, A) → CA
  5. Conic(Pae, Pbe, Pce, A, B) → circumellipse
  6. Center(circumellipse) → Ue
  7. Conic(Ap, Bp, Cp, Pai, Pbi) → inellipse
  8. Center(inellipse) → Ui
  9. FirstAxis(circumellipse) → majoraxisce
  10. FirstAxis(inellipse) → majoraxisie
  11. SecondAxis(circumellipse) → minoraxisce
  12. SecondAxis(inellipse) → minoraxisie
  13. Focus(circumellipse) → F1ce, F2ce
  14. Focus(inellipse) → F1ie, F2ie