欧拉线与九点圆：共线与切线构型的动态几何

GeoGebra 命令及参数

1. Intersect(yAxis, xAxis) → A
2. Polygon(A, B, C) → t1, c, a_1, b_1
3. OrthogonalLine(A, a_1) → f
4. OrthogonalLine(B, b_1) → g
5. OrthogonalLine(C, c) → h
6. Intersect(h, g) → Ortocentro
7. Intersect(f, a_1) → H
8. Intersect(h, c) → K
9. Intersect(b_1, g) → T
10. Angle(B, K, C) → α
11. Angle(C, H, A) → β
12. Angle(B, T, C) → γ
13. Midpoint(C, B) → P
14. Midpoint(B, A) → N
15. Midpoint(C, A) → M
16. Segment(P, A) → i
17. Segment(C, N) → j
18. Segment(B, M) → k
19. Intersect(i, t1) → D, D_1
20. Intersect(k, j) → Baricentro
21. AngularBisector(A, C, B) → l
22. AngularBisector(B, A, C) → m
23. AngularBisector(C, B, A) → n
24. Intersect(m, n) → Incentro
25. OrthogonalLine(Incentro, b_1) → p
26. Intersect(p, b_1) → E
27. Circle(Incentro, E) → d
28. OrthogonalLine(P, a_1) → q
29. OrthogonalLine(M, b_1) → r
30. OrthogonalLine(N, c) → s
31. Intersect(r, q) → Circocentro
32. Angle(Circocentro, M, C) → δ
33. Angle(B, N, Circocentro) → ε
34. Point(q) → F
35. Angle(F, P, B) → ζ
36. Circle(Circocentro, A) → e
37. Conic(M, H, P, N, K) → t
38. Midpoint(C, Ortocentro) → G
39. Midpoint(Ortocentro, B) → I
40. Midpoint(Ortocentro, A) → J
41. Line(Ortocentro, Baricentro) → RettaEulero
42. Center(t) → O
43. Segment(C, M) → f_1
44. Segment(M, A) → g_1
45. Segment(A, N) → h_1
46. Segment(N, B) → i_1
47. Segment(C, P) → j_1
48. Segment(P, B) → k_1
49. Segment(C, K) → l_1
50. Segment(H, A) → m_1
51. Segment(B, T) → n_1
52. Segment(C, N) → p_1
53. Segment(P, A) → q_1
54. Segment(M, B) → r_1
55. Segment(P, K) → s_1
56. Segment(N, H) → t_1
57. Intersect(a_1, k_1) → L
58. Intersect(r, a_1) → Q
59. Segment(M, Q) → c_1
60. Point(t) → R
61. Point(RettaEulero) → S