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Langley's Problem

Langley's Problem
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2017-04-07 04:48
TriangleAngleGeometric Construction
This example demonstrates Langley's problem, a classic geometric puzzle involving angles and triangles. Using commands like rotation, circle, and polygon, users can explore angle relationships and geometric properties. Suitable for middle and high school students studying geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Rotate(B, 20°, A) → C
  2. Circle(A, B) → c_2
  3. Polygon(A, B, C) → poly1, c, a, b
  4. Intersect(Line[C, Rotate[A, 30°, C]], c) → F
  5. Intersect(Line[B, Rotate[A, -20°, B]], b) → E
  6. Segment(F, E) → f
  7. Segment(B, E) → g
  8. Segment(C, F) → h
  9. Angle(B, A, C) → BAC
  10. Angle(C, B, A) → CBA
  11. Angle(A, C, B) → ACB
  12. Angle(E, B, F) → EBF
  13. Angle(E, C, F) → ECF
  14. Intersect(Line[B, Rotate[C, 20°, B]], b) → G
  15. Segment(B, G) → i
  16. Segment(G, F) → j
  17. Angle(G, B, F) → GBF
  18. Angle(G, B, E) → GBE
  19. Angle(B, E, G) → BEG
  20. Angle(E, G, F) → FGE
  21. Angle(C, B, G) → CBG
  22. Segment(B, C) → k
  23. Segment(B, G) → l
  24. Segment(B, F) → m
  25. Segment(G, E) → n
  26. Angle(F, E, C) → GEF
  27. Angle(F, E, B) → BEF
  28. Angle(F, E, B) → FEB