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Incircle and excircles of a triangle

Incircle and excircles of a triangle
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2016-01-15 08:12
TriangleCircleGeometric Construction
This example demonstrates the incircle and excircles of a triangle of any shape. It involves key mathematical concepts such as the incircle and excircles of a triangle. The construction highlights the use of Polygon, AngularBisector, Intersect, and Circle commands in GeoGebra. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Line(B, A) → d
  3. Line(C, A) → e
  4. Line(C, B) → f
  5. AngularBisector(C, A, B) → g
  6. AngularBisector(C, B, A) → k
  7. AngularBisector(A, C, B) → h
  8. Intersect(g, k) → D
  9. OrthogonalLine(D, b) → i
  10. Intersect(e, i) → E
  11. Circle(D, E) → p
  12. Point(e) → F
  13. AngularBisector(F, A, B) → j
  14. Point(d) → H
  15. AngularBisector(C, B, H) → l
  16. Intersect(g, l) → I
  17. Intersect(p, f, 1) → J
  18. OrthogonalLine(I, d) → m
  19. Intersect(d, m) → K
  20. Circle(I, K) → r
  21. Intersect(k, j) → G
  22. OrthogonalLine(G, f) → n
  23. Intersect(f, n) → L
  24. Circle(G, L) → q
  25. AngularBisector(L, C, A) → s
  26. Intersect(h, j) → M
  27. OrthogonalLine(M, c) → t
  28. Intersect(d, t) → N
  29. Circle(M, N) → c_1