Longchamps点：三角形的特殊点与欧拉线性质演示

GeoGebra 命令及参数

1. Polygon(A, B, C) → T_{ABC}, c, a, b
2. Ellipse(C, B, A) → Ωa
3. Ellipse(A, C, B) → Ωb
4. Ellipse(A, B, C) → Ωc
5. Intersect(Ωb, Ωc, 2) → D
6. Intersect(Ωb, Ωc, 1) → E
7. Segment(D, E) → g
8. Intersect(Ωa, Ωb, 2) → F
9. Intersect(Ωa, Ωb, 1) → G_1
10. Segment(F, G_1) → h
11. Intersect(Ωa, Ωc, 1) → H_1
12. Intersect(Ωa, Ωc, 2) → I_1
13. Segment(H_1, I_1) → i
14. TriangleCenter(A, B, C, 20) → Lo
15. Line(A, a) → j
16. Line(B, b) → k
17. Line(C, c) → l
18. Intersect(k, l) → A'
19. Intersect(j, l) → B'
20. Intersect(j, k) → C'
21. OrthogonalLine(A', j) → m
22. OrthogonalLine(C', l) → n
23. OrthogonalLine(B', k) → p
24. Circle(B, A, C) → q
25. TriangleCenter(A, B, C, 1) → I
26. TriangleCenter(A, B, C, 2) → G
27. TriangleCenter(A, B, C, 4) → H
28. TriangleCenter(A, B, C, 7) → Ge
29. Line(Ge, I) → r
30. Line(H, G) → s
31. TriangleCenter(A, B, C, 3) → O
32. Segment(C', A') → f_1
33. Segment(A', B') → g_1
34. Segment(B', C') → h_1
35. TriangleCenter(A, B, C, 5) → N
36. TriangleCenter(A, B, C, 175) → J
37. TriangleCenter(A, B, C, 176) → K
38. Circle(A, a) → c_1
39. Circle(B, b) → d_1
40. Circle(C, c) → e_1
41. Intersect(c_1, e_1) → L, M, ,
42. Line(M, L) → i_1
43. Intersect(c_1, d_1) → Q, R, ,
44. Line(Q, R) → j_1
45. Intersect(d_1, e_1) → P, S, ,
46. Line(S, P) → k_1
47. Segment(A, Q) → l_1
48. Segment(B, P) → m_1
49. Segment(C, M) → n_1