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Ellipse Tangent to Kite

Ellipse Tangent to Kite
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2016-04-04 14:16
PolygonCoordinate GeometryGeometric Construction
This example demonstrates the geometric relationship between an ellipse and a kite where they are tangent to each other. Key math concepts include ellipse, kite, straight lines, and coordinate geometry. Construction involves commands like Segment, Mirror, Intersect, Ray, Line, Midpoint, Circle, and Ellipse in GeoGebra. Suitable for high school students and above to explore geometric constructions and properties of shapes.

GeoGebra Commands & Parameters

  1. Segment(Q, C) → a
  2. Mirror(B, a) → B'
  3. Segment(Q, B) → b
  4. Segment(B, C) → c
  5. Segment(C, B') → d
  6. Segment(B', Q) → e
  7. Segment(B, B') → f
  8. Intersect(a, f) → D
  9. Ray(C, B) → g
  10. Ray(B', Q) → h
  11. Ray(B, Q) → i
  12. Ray(C, B') → j
  13. Intersect(g, h) → E
  14. Intersect(i, j) → F
  15. Line(D, F) → k
  16. Line(D, E) → l
  17. Intersect(l, b) → P_1
  18. Intersect(k, c) → H
  19. Intersect(l, d) → I
  20. Intersect(k, e) → P_2
  21. Midpoint(P_1, H) → K
  22. Ray(B, K) → m
  23. Intersect(a, m) → O
  24. Line(O, f) → n
  25. Circle(Q, P_1, P_2) → p
  26. Intersect(p, n, 1) → F_1
  27. Intersect(p, n, 2) → F_2
  28. Ellipse(F_1, F_2, P_2) → q
  29. Segment(E, I) → r
  30. Segment(H, F) → s
  31. Segment(P_1, H) → t
  32. Segment(B, O) → a_1