欧拉线与直极点椭圆的几何作图

GeoGebra 命令及参数

1. Line(A, B) → f
2. Line(B, C) → g
3. Line(C, A) → h
4. TriangleCenter(A, B, C, 3) → O
5. TriangleCenter(A, B, C, 4) → H
6. Line(O, H) → s
7. Point(s) → D
8. Line(A, D) → i
9. Line(C, D) → j
10. Line(B, D) → k
11. Intersect(f, j) → E
12. Intersect(g, i) → F
13. Intersect(h, k) → G
14. Line(E, F) → l
15. Line(F, G) → m
16. Line(E, G) → n
17. Intersect(f, m) → H_{1}
18. Intersect(g, n) → I_{1}
19. Line(H_{1}, I_{1}) → p
20. Circle(D, 1) → d
21. Point(d) → O_{1}
22. Line(D, O_{1}) → t
23. OrthogonalLine(A, t) → a
24. OrthogonalLine(C, t) → b
25. OrthogonalLine(B, t) → e
26. Intersect(t, a) → P
27. Intersect(t, b) → Q
28. Intersect(t, e) → R
29. OrthogonalLine(P, g) → f_1
30. OrthogonalLine(R, h) → g_1
31. OrthogonalLine(Q, f) → h_1
32. Intersect(f_1, g_1) → S
33. Locus(S, O_{1}) → loc1
34. OrthogonalLine(D, h) → i_1
35. OrthogonalLine(D, f) → j_1
36. OrthogonalLine(D, g) → k_1
37. Intersect(h, i_1) → T
38. Intersect(j_1, f) → U
39. Intersect(g, k_1) → V
40. Circle(U, V, T) → c_1
41. Intersect(c_1, f, 2) → W
42. Intersect(c_1, g, 2) → Z
43. Intersect(c_1, h, 2) → A_1
44. OrthogonalLine(A_1, h) → l_1
45. OrthogonalLine(W, f) → m_1
46. OrthogonalLine(Z, g) → n_1
47. Intersect(l_1, n_1) → B_1
48. LocusEquation(S, O_{1}) → o
49. TriangleCenter(A, B, C, 11) → M
50. TriangleCenter(A, B, C, n_2) → N
51. TriangleCenter(A, B, C, 1) → I
52. OrthogonalLine(I, f) → p_1
53. Intersect(p_1, f) → D_1
54. Circle(I, D_1) → d_1
55. Conic(A, B, C, O, H) → c