Feuerbach Theorem: Incircle and Nine-Point Circle of Triangle

GeoGebra Commands & Parameters

1. Line(B, C) → a
2. Line(A, B) → c
3. Midpoint(B, C) → A'
4. Midpoint(C, A) → B'
5. Midpoint(A, B) → C'
6. OrthogonalLine(A, a) → d
7. Intersect(a, d) → D
8. C_Inscrit(B, A, C) → I, e_2
9. Circle(C', B', D) → f
10. Segment(B', D) → j
11. LineBisector(D, A') → g
12. Intersect(f, g, 2) → Q
13. Ray(A, I) → k
14. Intersect(a, k) → W
15. Segment(A', B') → h
16. Angle(B', A', D) → α
17. Angle(C, D, B') → β
18. Angle(A, C, D) → γ
19. Segment(Q, A') → i
20. Angle(A', B', C) → δ
21. Angle(B, A, B') → ε
22. Circle(A, B, C) → p
23. Intersect(p, k, 2) → P
24. Center(f) → N
25. OrthogonalLine(P, a) → l
26. Intersect(p, l, 2) → P'
27. Line(A, P') → m
28. Intersect(g, m) → E
29. Line(A', Q) → n
30. Intersect(m, n) → F
31. OrthogonalLine(N, k) → q
32. Intersect(q, k) → L
33. Angle(A, L, N) → ζ
34. Intersect(n, q) → M
35. Intersect(q, l) → U
36. OrthogonalLine(I, l) → r
37. Intersect(l, r) → V
38. OrthogonalLine(I, a) → s
39. Intersect(a, s) → J
40. Segment(A, B) → b_1
41. Segment(B, C) → c_1
42. Segment(C, A) → d_1
43. Segment(A', J) → f_1
44. Segment(P, U) → pu
45. Segment(P, N) → pn
46. Segment(P, I) → pei
47. Segment(P, V) → pv
48. Circle(I, L, V) → g_1
49. Segment(P, L) → pl
50. Segment(I, N) → pin
51. Segment(L, I) → pli
52. OrthogonalLine(P', d_1) → t
53. Intersect(t, d_1) → K
54. Segment(P', K) → a_1
55. Segment(A, K) → e_1
56. Angle(P', K, A) → η
57. Polygon(Q, U, A', N) → poly1, q_1, u, a', n_1
58. Polygon(A, K, P') → poly2, p', a_2, k_1
59. Angle(A', K, C) → θ
60. Angle(W, A, C) → ι
61. Angle(P, P', C) → κ
62. Segment(P', C) → b
63. Circle(A', K, P') → h_1
64. Polygon(A', K, P', C) → poly3, a'_1, k_2, p'_1, c_2
65. Segment(I, J) → i_1