丹德林定理的GeoGebra三维演示：圆锥截面与内切球

GeoGebra 命令及参数

1. InfiniteCone((0, 0, 0), zAxis, α) → a
2. Axes(a) → d, e, f
3. Rotate(f, (-α), yAxis) → f'_1
4. Point(f'_1) → A
5. Rotate(f, α, yAxis) → f'
6. Point(f') → B
7. Plane(A, B_1, B) → b
8. IntersectPath(b, a) → c
9. Axes(c) → i, j
10. AngularBisector(f', i) → b2, b1
11. Center(a) → O
12. Vector(O, B) → vOB
13. Angle(Vector[A, B], Vector[A, O]) → β
14. Vector(O, A) → vOA
15. Rotate(vOA, β / 2, A, k) → vOA'
16. Angle(Vector[B, A], Vector[O, B]) → α1
17. Rotate(vOB, α1 / 2, B, k) → vOB'
18. Ray(B, B') → g
19. Intersect(f, b1) → G
20. OrthogonalLine(G, i, k) → h
21. Intersect(i, h) → H
22. Circle(G, H, k) → p
23. Sphere(G, H) → l
24. Ray(A, A') → m
25. Intersect(f, b2) → L
26. OrthogonalLine(L, i, k) → n
27. Intersect(i, n) → M
28. Circle(L, M, k) → s
29. Point(c) → P
30. Line(O, P) → a_1
31. Segment(M, P) → b_1
32. Segment(P, H) → e_1
33. Sphere(L, M) → l'
34. OrthogonalLine(L, f'_1, k) → q
35. OrthogonalLine(G, f'_1, k) → r
36. Intersect(f'_1, r) → C
37. Intersect(q, f'_1) → D
38. Circle(f, C) → t
39. Circle(f, D) → c_1
40. Line(O, P) → d_1
41. Intersect(d_1, c_1) → E,
42. Intersect(d_1, t) → F,
43. Segment(P, F) → f_1
44. Segment(E, P) → g_1
45. Segment(O, E) → h_1