圆锥曲线与角度/向量几何的交互作图任务

GeoGebra 命令及参数

1. Polygon(A, B, C) → t1, c, a, b
2. OrthogonalLine(C, b) → f
3. Circle(C, 1) → d
4. Intersect(d, f, 1) → D
5. Segment(A, D) → g
6. OrthogonalLine(D, g) → h
7. Circle(D, 1) → e
8. Intersect(e, h, 2) → E
9. Segment(A, E) → i
10. OrthogonalLine(E, i) → j
11. Circle(E, 1) → k
12. Intersect(k, j, 2) → F
13. Segment(A, F) → l
14. OrthogonalLine(F, l) → m
15. Circle(F, 1) → p
16. Intersect(p, m, 2) → G
17. Segment(A, G) → n
18. OrthogonalLine(G, n) → q
19. Circle(G, 1) → r
20. Intersect(r, q, 2) → H
21. Segment(A, H) → s
22. OrthogonalLine(H, s) → t
23. Circle(H, 1) → c_1
24. Intersect(c_1, t, 2) → I
25. Segment(A, I) → f_1
26. OrthogonalLine(I, f_1) → g_1
27. Circle(I, 1) → d_1
28. Segment(C, D) → m_2
29. Segment(D, E) → n_2
30. Segment(E, F) → p_2
31. Segment(F, G) → q_2
32. Segment(G, H) → r_2
33. Segment(H, I) → s_2
34. Angle(C, B, A) → α
35. Angle(D, C, A) → β
36. Angle(E, D, A) → γ
37. Angle(F, E, A) → δ
38. Angle(G, F, A) → ε
39. Angle(H, G, A) → ζ
40. Angle(I, H, A) → η
41. Segment(A, B) → l_3
42. Segment(C, B) → m_3
43. Segment(C, A) → n_3
44. RotateText(text1_{1}, atand(Slope[n_3])) → text2
45. RotateText(text3, atand(Slope[g])) → text4
46. Midpoint(f_1) → S
47. RotateText(text5, pi / 4) → text6
48. RotateText(text7, atan(Slope[g])) → text8
49. RotateText(text9, atand(Slope[i])) → text10
50. Rotate(D, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → D'
51. Rotate(E, If[0 < o ≤ 1, ((-o) * pi / 3), ((-pi)) / 3], E) → E'
52. Segment(D', E') → p_3
53. Rotate(D', If[1 < o ≤ 2, ((-(o - 1)) * pi), (-pi)], D') → D''
54. Rotate(E', If[1 < o ≤ 2, ((o - 1) * pi), pi], D') → E''
55. Segment(D'', E'') → q_3
56. Dilate(A, If[3 < o ≤ 4, 4 - o, 0], I) → A'
57. Vector(A, A') → u
58. Translate(C, u) → C'
59. Translate(A, u) → A'_{1}
60. Segment(C', A'_{1}) → r_3
61. Translate(C, u) → C'_{1}
62. Angle(A, I, C'_{1}) → σ
63. Rotate(C', If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → C''
64. Rotate(A'_{1}, If[4 < o ≤ 5, ((-(o - 4)) * σ), (-σ)], I) → U
65. Segment(C'', U) → s_3
66. Segment(A, S) → t_3
67. Segment(S, I) → a_3
68. Rotate(C'', If[5 < o ≤ 6, ((o - 5) * pi), pi], S) → C'''
69. Rotate(U, If[5 < o ≤ 6, ((-(o - 5)) * pi), (-pi)], S) → U'
70. Segment(C''', U') → b_3
71. Polygon(A, B, C) → t2, c_4, a_4, b_4
72. Polygon(A, C, D) → t3, d_4, a_5, c_5
73. Polygon(A, D, E) → t4, e_4, a_6, d_5
74. Circle(A, Distance[A, C]) → k_4
75. Polygon(A, H, I) → t5, i_5, a_7, h_5
76. RotateText(text11, atand(Slope[t_3])) → text12