直角三角形中的圆与轨迹

GeoGebra 命令及参数

1. Segment(A, B) → f
2. Rotate(A, (a * π / 180), B) → A'
3. Angle(A, B, A') → α
4. Ray(B, A') → g
5. OrthogonalLine(A, f) → h
6. Intersect(h, g) → D
7. Polygon(B, A, D) → t1, d, b, a_1
8. Segment(B, D) → i
9. Angle(D, A, B) → β
10. Segment(A, D) → j
11. Rotate(A, α / 3, B) → A'_1
12. Angle(A, B, A'_1) → γ
13. Rotate(A'_1, α / 3, B) → C
14. Angle(A'_1, B, C) → δ
15. Ray(B, A'_1) → k
16. Ray(B, C) → l
17. Intersect(j, k) → E
18. OrthogonalLine(E, i) → m
19. Intersect(m, i) → F
20. OrthogonalLine(A, k) → n
21. Intersect(n, k) → G
22. Distance(A, G) → distanceAG
23. Distance(E, F) → distanceEF
24. Circle(B, (0.25 * f)) → c
25. Angle(B, G, A) → ε
26. Angle(B, F, E) → ζ
27. Midpoint(E, F) → H
28. Intersect(c, g) → I,
29. Intersect(c, l) → J,
30. Intersect(l, m) → K
31. Intersect(f, g) → L
32. Midpoint(B, K) → M
33. Dilate(B, If[0 < e ≤ 1, 1 - e, 0], E) → B'
34. Dilate(A, If[7.5 < e ≤ 8.5, 8.5 - e, 0], G) → A'_2
35. Segment(B, B') → p
36. Segment(A, A'_2) → q
37. Dilate(G, If[1 < e ≤ 2, 2 - e, 0], E) → G'
38. Dilate(B, If[1 < e ≤ 2, 2 - e, 0], M) → B'_1
39. Segment(B, B'_1) → r
40. Rotate(I, If[2 < e ≤ 3, ((-(e - 2)) * γ), (-γ)], B) → I'
41. CircleSector(B, I', I) → s
42. Rotate(s, If[4 < e ≤ 5, ((-(e - 4)) * γ), (-γ)], B) → s'
43. Rotate(s', If[6 < e ≤ 7, ((-(e - 6)) * γ), (-γ)], B) → s''
44. Dilate(E, If[9 < e ≤ 10, 10 - e, 0], H) → E'
45. Segment(E, E') → t
46. Dilate(H, If[10 < e ≤ 11, 11 - e, 0], F) → H'
47. Segment(H, H') → f_1
48. Line(F, q) → g_1
49. Intersect(g_1, p) → N
50. Angle(N, F, E) → η
51. Dilate(G, If[11.5 < e ≤ 12.5, 12.5 - e, 0], F) → G'_1
52. Vector(G, G'_1) → u
53. Translate(A, u) → A'_3
54. Translate(A'_2, u) → O
55. Translate(A, u) → A'_4
56. Translate(A'_2, u) → P
57. Segment(A'_4, P) → q'
58. Rotate(A'_4, If[12.5 < e ≤ 13.5, ((e - 12.5) * η), η], F) → Q
59. Rotate(P, If[12.5 < e ≤ 13.5, ((e - 12.5) * η), η], F) → P'
60. Segment(Q, P') → q''
61. Dilate(G, If[13.5 < e ≤ 14.5, 14.5 - e, 0], H) → G'_2
62. Vector(G, G'_2) → v
63. Translate(A, v) → A'_5
64. Translate(A'_2, v) → R
65. Segment(A'_5, R) → q'_1
66. Rotate(A'_5, If[14.5 < e ≤ 15.5, ((e - 14.5) * η), η], H) → S
67. Rotate(R, If[14.5 < e ≤ 15.5, ((e - 14.5) * η), η], H) → R'
68. Segment(S, R') → h_1