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Incircle, Excircles, and Nagel Point

Incircle, Excircles, and Nagel Point
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2015-02-12 06:27
TriangleCircleGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the four tritangent circles (incircle and three excircles) of a triangle and the Nagel point. The Nagel point is the point of concurrency of the segments joining the vertices of a triangle to the points where the excircles touch the opposite sides. This example involves the concepts of incircle, excircles, and the Nagel point, using Segment, AngularBisector, Intersect, OrthogonalLine, Circle, and Line commands in GeoGebra. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(B, C) → b
  3. Segment(C, A) → c
  4. AngularBisector(A, B, C) → d
  5. AngularBisector(C, A, B) → e
  6. AngularBisector(B, C, A) → f
  7. Intersect(d, e) → I
  8. OrthogonalLine(I, c) → g
  9. Intersect(g, c) → D
  10. Circle(I, D) → h
  11. Intersect(h, a, 1) → E
  12. Intersect(h, b, 1) → F
  13. Line(A, B) → i
  14. Line(B, C) → j
  15. Line(C, A) → k
  16. OrthogonalLine(B, d) → l
  17. OrthogonalLine(A, e) → m
  18. Intersect(e, l) → G
  19. Intersect(f, l) → H
  20. Intersect(d, m) → J
  21. OrthogonalLine(G, j) → p
  22. OrthogonalLine(H, i) → n
  23. OrthogonalLine(J, k) → q
  24. Intersect(i, n) → K
  25. Circle(H, K) → r
  26. Intersect(k, q) → L
  27. Circle(J, L) → s
  28. Intersect(j, p) → M
  29. Circle(G, M) → t
  30. OrthogonalLine(C, f) → a_1
  31. Segment(K, C) → b_1
  32. Segment(B, L) → c_1
  33. Segment(A, M) → d_1
  34. Intersect(b_1, c_1) → N