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Inscribed Conic with Symmedian as Center

Inscribed Conic with Symmedian as Center
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2015-02-17 09:08
TriangleCoordinate GeometryGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates an inscribed conic with the symmedian K as its center, which is tangent to the sides of the triangle at the vertices of the orthic triangle. Key concepts include triangle, symmedian, and inscribed conic. The construction uses GeoGebra commands such as Line, Polygon, Midpoint, OrthogonalLine, and Intersect. Suitable for high school geometry education.

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. Midpoint(A, C) → E
  6. Midpoint(C, B) → F
  7. Midpoint(B, A) → H_1
  8. OrthogonalLine(A, b) → i
  9. OrthogonalLine(B, c) → j
  10. OrthogonalLine(C, a) → k
  11. Intersect(i, j) → H
  12. Intersect(a, k) → M
  13. Intersect(c, j) → N
  14. Intersect(b, i) → O
  15. Polygon(M, N, O) → poly2, o, m, n
  16. Centroid(poly1) → G
  17. Mirror(G, c) → G'_4
  18. Mirror(G, a) → G'_1
  19. Mirror(G, b) → G'_2
  20. LineBisector(G'_1, G'_4) → d
  21. LineBisector(G'_4, G'_2) → e
  22. Intersect(d, e) → K
  23. Mirror(G, K) → G'
  24. Mirror(O, K) → O'
  25. Mirror(M, K) → M'
  26. Mirror(N, K) → N'
  27. Conic(M', N, O', M, O) → f