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Incenter Exploration by Cheris South

Incenter Exploration by Cheris South
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2016-11-29 20:50
TriangleCircleGeometric Construction
This example demonstrates a dynamic investigation of the incircle of a triangle. Key mathematical concepts include the incircle of a triangle, angles, and geometric construction. Using GeoGebra commands such as Segment, PointIn, and Polygon, the relationship between the incircle and the triangle can be observed dynamically. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Slope(f) → m
  3. PointIn(b) → C
  4. Segment(B, C) → g
  5. Segment(C, A) → h
  6. Polygon(A, B, C) → poly1, c, a_1, b_1
  7. Angle(poly1) → α, β, γ
  8. Rotate(B, α / 2, A) → B'
  9. Angle(B, A, B') → δ
  10. Line(A, B') → i
  11. Intersect(g, i) → D
  12. Rotate(A, γ / 2, C) → A'
  13. Angle(A, C, A') → ε
  14. Line(C, A') → j
  15. Intersect(j, f) → E
  16. Rotate(C, β / 2, B) → C'
  17. Angle(C, B, C') → ζ
  18. Line(B, C') → k
  19. Intersect(k, h) → F
  20. Ray(C, E) → n
  21. Ray(B, F) → p
  22. Intersect(p, n) → I
  23. Angle(I, A, C) → η
  24. Angle(E, C, B) → θ
  25. Angle(F, B, A) → ι
  26. Ray(A, I) → l
  27. Line(A, C) → q
  28. Slope(q) → m_1