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Incenter & Incircle Dynamic Exploration by Tim Brzezinski

Incenter & Incircle Dynamic Exploration by Tim Brzezinski
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2016-06-06 17:52
CircleAngleGeometric ConstructionSlider AnimationLocus
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Triangle Theorems
This example demonstrates the dynamic behavior of the incenter and incircle of a triangle, highlighting key mathematical concepts such as incenter, incircle, angles, linear regression, set theory, hypergeometric distribution, unit circle, and random experiments. The construction utilizes GeoGebra commands like Segment, Slope, PointIn, Polygon, Angle, Rotate, Line, Intersect, and Ray, involving objects A, B, f, m, a, b, C, g, h, poly1, c, a_1, b_1, α, β, γ, B', δ, i, D, A', ε, j, E, C', ζ, k, F, n, p, I, η, θ, ι, l, q, m_1, d. Suitable for high school and advanced learners exploring the intersection of geometry and probability statistics.

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