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Triangle Area = Radius of Inscribed Circle Times Perimeter

Triangle Area = Radius of Inscribed Circle Times Perimeter
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2015-11-15 09:25
TriangleCircleTrigonometryGeometric Construction
This example demonstrates the relationship between the area of a triangle and the product of the radius of the inscribed circle and the perimeter. Key mathematical concepts include triangle area, inscribed circle radius, and perimeter. Using GeoGebra commands such as Polygon, AngularBisector, and Intersect, the construction of the triangle and its inscribed circle is shown, illustrating this geometric property. Suitable for middle school and above students learning geometry and trigonometric functions.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. AngularBisector(C, A, B) → d
  3. AngularBisector(A, C, B) → e
  4. AngularBisector(C, B, A) → f
  5. Intersect(d, e) → D
  6. OrthogonalLine(D, b) → g
  7. OrthogonalLine(D, a) → h
  8. OrthogonalLine(D, c) → i
  9. Intersect(h, a) → E
  10. Intersect(f, g) → F
  11. Intersect(i, c) → G
  12. Intersect(g, b) → H
  13. Segment(D, G) → j
  14. Segment(D, H) → k
  15. Segment(D, E) → l
  16. Circle(D, H) → p
  17. Polygon(A, D, B) → poly2, b_1, a_1, d_1
  18. Polygon(D, C, B) → poly3, b_2, d_2, c_1
  19. Polygon(A, D, C) → poly4, c_2, a_2, d_3
  20. Angle(D, E, B) → α
  21. Angle(D, G, A) → β
  22. Angle(D, H, C) → γ
  23. Angle(D, C, B) → δ
  24. Angle(A, C, D) → ε
  25. Angle(D, A, C) → ζ
  26. Angle(B, A, D) → η
  27. Angle(C, B, D) → θ
  28. Angle(D, B, A) → ι