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Locus of the Intersection Point of Angle Bisectors

Locus of the Intersection Point of Angle Bisectors
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2015-03-24 00:22
TriangleCircleAngleGeometric ConstructionLocus
When point A, a vertex of the triangle, moves along the arc of a circle, what is the locus of the intersection point G of the angle bisectors? This example demonstrates the locus of the intersection point of angle bisectors. Key concepts include triangle, circle, angle bisector, and locus. GeoGebra commands used include Circle, Point, Segment, Angle, Rotate, Line, and Intersect. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Circle(L, T) → c
  2. Point(c) → A
  3. Point(c) → B
  4. Point(c) → C
  5. Segment(A, B) → a
  6. Segment(B, C) → b
  7. Segment(C, A) → d
  8. Angle(B, A, C) → α
  9. Angle(A, C, B) → β
  10. Angle(C, B, A) → γ
  11. Rotate(C, (-(α / 2)), A) → C'
  12. Angle(C', A, C) → δ
  13. Rotate(C, γ / 2, B) → C'_1
  14. Angle(C, B, C'_1) → ε
  15. Rotate(A, β / 2, C) → A'
  16. Angle(A, C, A') → ζ
  17. Line(B, C'_1) → e
  18. Line(C, A') → f
  19. Line(A, C') → g
  20. Intersect(e, d) → D
  21. Intersect(g, b) → E
  22. Intersect(a, f) → F
  23. Segment(B, D) → h
  24. Segment(A, E) → i
  25. Segment(C, F) → j
  26. Intersect(h, i) → G