Dandelin圆：解析几何中的经典构造

GeoGebra 命令及参数

1. Point(zAxis) → S
2. Intersect(yAxis, zAxis) → C_1
3. Mirror(C_1, S) → C_2
4. Line(C_1, D) → g
5. Line(C_2, g) → h
6. Plane(h, g) → p
7. Point(xAxis) → A
8. Cone(C_1, S, Distance[C_1, A]) → a, a_{2}, a_{3}
9. Mirror(a_{3}, S) → b
10. Mirror(a_{2}, S) → c
11. Line(C_1, C_2) → f
12. PointIn(p) → B_1
13. OrthogonalLine(B_1, p) → i
14. PointIn(p) → B_2
15. Plane(B_2, i) → q
16. IntersectPath(q, b) → d
17. IntersectPath(q, a) → e
18. Corner(e) → E, F
19. Line(B_2, B_1) → j
20. Intersect(g, a_{2}, 2) → K_1
21. Intersect(h, c, 1) → K_2
22. Line(K_1, K_2) → k
23. Mirror(k, f) → k'
24. Intersect(k', a_{2}, 1) → L_1
25. Intersect(h, c, 2) → L_2
26. AngularBisector(k', j) → l, m
27. Intersect(l, f) → O_1
28. OrthogonalLine(O_1, j, space) → n
29. Intersect(n, q) → F_1
30. Sphere(O_1, F_1) → o
31. AngularBisector(j, k) → r, s
32. Intersect(r, f) → O_2
33. OrthogonalLine(O_2, j, space) → t
34. Intersect(t, j) → F_2
35. Sphere(O_2, F_2) → u
36. OrthogonalLine(O_2, k', space) → f_1
37. OrthogonalLine(O_1, k, space) → g_1
38. Intersect(g_1, k) → B
39. Intersect(f_1, k') → C
40. Circle(f, B) → c_1
41. Circle(f, C) → d_1
42. Point(e) → M
43. Line(M, S) → h_1
44. Intersect(h_1, d_1, 1) → Q_1
45. Intersect(h_1, c_1, 1) → Q_2
46. Segment(F_2, M) → i_1
47. Segment(Q_1, M) → j_1
48. Segment(M, F_1) → k_1
49. Segment(M, Q_2) → l_1
50. Plane(d_1) → p_1
51. IntersectPath(p_1, q) → m_1
52. Point(c_1) → G
53. Point(c_1) → H
54. Point(c_1) → I
55. Plane(G, H, I) → q_1
56. IntersectPath(q, q_1) → n_1
57. Intersect(j, m_1) → J
58. Intersect(n_1, j) → K
59. Plane(d_1) → r_1
60. IntersectPath(r_1, q) → s_1
61. Intersect(s_1, j) → L