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Maximum Perimeter Property of the Incircle

Maximum Perimeter Property of the Incircle
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2017-04-18 22:13
TriangleCircleOptimization
This example demonstrates the maximum perimeter property of the incircle. Key mathematical concepts include circles, triangles, and perimeter. Using GeoGebra commands such as Circle, Point, Segment, and Tangent, the construction of the incircle and the observation of its perimeter changes are illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(P, ra) → ca
  2. Circle(P, rb) → cb
  3. Circle(P, rc) → cc
  4. Point(ca) → A
  5. Point(cb) → B
  6. Point(cc) → C
  7. Segment(B, A) → f
  8. Segment(A, C) → g
  9. Segment(C, B) → h
  10. Segment(P, A) → i
  11. Segment(B, P) → j
  12. Segment(P, C) → k
  13. Angle(B, A, P) → α
  14. Angle(P, A, C) → β
  15. Angle(A, C, P) → γ
  16. Angle(P, C, B) → δ
  17. Angle(C, B, P) → ε
  18. Angle(P, B, A) → ζ
  19. Tangent(B, cb) → l,
  20. Tangent(C, cc) → m,
  21. Tangent(A, ca) → n,
  22. Ellipse(C, A, B) → e