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Central Conic Cevian Complement

Central Conic Cevian Complement
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2015-02-16 22:04
CircleCoordinate GeometryGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the construction of a conic centered at point P with another point Q as its central cevian. Key math concepts include conics, central points, and geometric constructions. It utilizes GeoGebra commands like Line, OrthogonalLine, Intersect, Midpoint, Mirror, and Conic. Suitable for high school students and geometry enthusiasts exploring conic properties and special point constructions.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. OrthogonalLine(Q_1, a) → g
  5. OrthogonalLine(Q_1, c) → h
  6. OrthogonalLine(Q_1, b) → i
  7. Intersect(b, i) → I
  8. Midpoint(A, C) → M
  9. Midpoint(C, B) → N
  10. Midpoint(B, A) → O_1
  11. Line(B, P) → k
  12. Line(C, P) → s
  13. Line(A, P) → t
  14. Intersect(a, s) → D
  15. Intersect(c, k) → G_1
  16. Intersect(b, t) → H
  17. Mirror(H, P) → H'
  18. Mirror(G_1, P) → G
  19. Mirror(D, P) → D'
  20. Conic(H', D, G, H, D') → p
  21. Intersect(p, b, 2) → E
  22. Intersect(p, c, 1) → F
  23. Intersect(p, a, 2) → J
  24. Line(J, C) → d
  25. Line(E, A) → e
  26. Line(F, B) → f
  27. Intersect(d, e) → Q