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Excircles and the Nagel Point

Excircles and the Nagel Point
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2015-02-12 06:31
TriangleCircleGeometric Construction
In collections A Tour of Triangle Geometry
This example demonstrates the geometric relationship between excircles and the Nagel point of a triangle. Key concepts include excircles, tangency points, Nagel point, angle bisectors, intersections. Construction involves commands like Segment, AngularBisector, Intersect, OrthogonalLine, Circle, Line, Ray. Suitable for high school and above mathematics learners to explore advanced triangle geometry properties.

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
  35. Intersect(s, i, 1) → O
  36. Intersect(s, j, 2) → P
  37. Segment(A, P) → e_1
  38. Segment(C, O) → f_1
  39. Ray(B, L) → g_1
  40. Intersect(e_1, f_1) → Q