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Incircle Radius and Excircle Radii Inverses

Incircle Radius and Excircle Radii Inverses
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2016-08-23 09:42
TriangleCircleGeometric Construction
This example demonstrates the relationship between the radius of the incircle and the sum of the inverses of the radii of the excircles in a triangle. It involves core concepts like incircle, excircles, inverse operations, and geometric constructions. The construction uses commands such as Line, AngularBisector, Intersect, OrthogonalLine, Circle, and Segment. Suitable for high school mathematics education to understand the geometric properties of incircles and excircles in triangles.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(B, C) → b
  3. Line(C, A) → c
  4. AngularBisector(b, a) → d, e
  5. AngularBisector(c, a) → f, g
  6. Intersect(f, d) → D
  7. Intersect(e, g) → E
  8. AngularBisector(c, b) → h, i
  9. Intersect(g, d) → F
  10. Intersect(e, f) → G
  11. OrthogonalLine(E, b) → j
  12. Intersect(b, j) → H
  13. Circle(E, H) → k
  14. OrthogonalLine(F, b) → l
  15. Intersect(b, l) → I
  16. Circle(F, I) → p
  17. OrthogonalLine(G, c) → m
  18. Intersect(c, m) → J
  19. OrthogonalLine(D, a) → n
  20. Intersect(n, a) → K
  21. Circle(D, K) → q
  22. Circle(G, J) → r_1
  23. Segment(G, J) → R_b
  24. Segment(E, H) → r
  25. Segment(F, I) → R_a
  26. Segment(D, K) → R_c