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Ellipse Reflective Property by Tim Brzezinski (2)

Ellipse Reflective Property by Tim Brzezinski (2)
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2016-04-04 21:13
Angle
In collections Conic Sections Conic Sections- Maths Made Easy
This applet illustrates the reflective property of an ellipse, where segments drawn to the point of tangency of a tangent create congruent angles. Key concepts include ellipses, angles, and geometric construction. It utilizes commands like Ellipse, Tangent, Segment, and Angle in GeoGebra. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Ellipse(A, B, C) → c
  2. Point(c) → P
  3. Tangent(P, c) → a,
  4. Segment(A, P) → b
  5. Segment(B, P) → d
  6. Circle(P, 1) → e
  7. Intersect(e, b, 1) → E
  8. Intersect(e, a) → F, G
  9. Intersect(e, d, 1) → H
  10. Angle(F, P, E) → α
  11. Angle(H, P, G) → β
  12. CircleSector(P, F, E) → f
  13. Rotate(f, (g * γ), P) → f'
  14. CircleSector(P, F, H) → k
  15. Dilate(A, If[-2 < g ≤ -1, -1 - g, 0], P) → A'
  16. Segment(A, A') → i
  17. Dilate(B, If[-1 < g ≤ 0, (-g), 0], P) → B'
  18. Segment(B, B') → j
  19. Rotate(F, If[-1 < g ≤ 0, ((g + 1) * α), α], P) → F'
  20. CircleSector(P, F, F') → q
  21. Rotate(q, If[0.5 < g ≤ 1.5, ((g - 0.5) * (π - α)), π - α], P) → q'
  22. Intersect(e, a, 2) → D
  23. Intersect(α, a, 1) → I
  24. Point(a) → J
  25. Angle(J, P, B) → ε
  26. Intersect(e, i) → K,
  27. Rotate(D, If[-1 < g ≤ 0, ((-(g + 1)) * ε), (-ε)], P) → D'
  28. CircleSector(P, D', D) → r
  29. Rotate(r, If[0.5 < g ≤ 1.5, ((-(g - 0.5)) * (π - ε)), ε - π], P) → r'