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Dynamic Geometry Problem: Cut-The-Knot Action 18!

Dynamic Geometry Problem: Cut-The-Knot Action 18!
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2018-02-11 06:32
Coordinate GeometryComplex NumberGeometric Construction
This is a dynamic and modifiable geometric problem example that illustrates a problem posted by Alexander Bogomolny on Twitter. The example involves quadratic equations, expected value, hyperbola, and complex numbers. Using GeoGebra commands such as Point, Polygon, OrthogonalLine, etc., it demonstrates geometric transformations and construction points. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Point(c) → B
  3. Point(c) → C
  4. Polygon(B, A, C) → t1, c_1, b, a
  5. OrthogonalLine(B, b) → f
  6. OrthogonalLine(A, a) → g
  7. Line(B, C) → h
  8. Line(C, A) → i
  9. Line(A, B) → j
  10. Intersect(h, g) → D
  11. Intersect(f, i) → E
  12. Intersect(f, g) → F
  13. Dilate(A, If[0 < d ≤ 1, 1 - d, 0], B) → A'
  14. Dilate(B, If[0 < d ≤ 1, 1 - d, 0], C) → B'
  15. Dilate(C, If[0 < d ≤ 1, 1 - d, 0], A) → C'
  16. Segment(A, A') → k
  17. Segment(B, B') → l
  18. Segment(C, C') → m
  19. Dilate(A, If[2 < d ≤ 3, 3 - d, 0], D) → A'_1
  20. Dilate(B, If[2 < d ≤ 3, 3 - d, 0], E) → B'_1
  21. Segment(B, B'_1) → n
  22. Segment(A, A'_1) → p
  23. Angle(A, E, B) → α
  24. Angle(A, D, C) → β