几何作图综合：圆与变换下的角度/三角函数关系

GeoGebra 命令及参数

1. Circle(A, B) → c
2. Intersect(c, q) → O, P
3. CircleArc(A, O, P) → d
4. Point(d) → C
5. CircleArc(A, C, P) → e
6. Point(e) → D
7. Dilate(A, If[0 < j ≤ 1, 1 - j, 0], C) → A'
8. Segment(A, A') → a
9. Angle(C, A, D) → α
10. Rotate(A, If[1 < j ≤ 2, ((j - 1) * α), α], A) → A'_1
11. Rotate(A', If[1 < j ≤ 2, ((j - 1) * α), α], A) → A''
12. Segment(A'_1, A'') → a'
13. Segment(A, C) → b
14. Segment(C, D) → f
15. Segment(D, A) → g
16. Midpoint(f) → E
17. Segment(A, E) → h
18. Midpoint(h) → F
19. Segment(A, F) → i
20. Segment(F, E) → k
21. Circle(A, (0.35 * i)) → p
22. Circle(E, (0.15 * Distance[D, E])) → r
23. Intersect(r, f, 2) → G
24. Intersect(r, h, 1) → H
25. Intersect(r, f, 1) → I
26. Intersect(p, b, 1) → J
27. Intersect(p, h, 1) → K
28. Intersect(p, g, 1) → L
29. Circle(A, B) → c_1
30. Dilate(C, If[2 < j ≤ 3, 3 - j, 0], D) → C'
31. Segment(C, C') → l
32. Polygon(C, D, A) → poly1, a_1, c_2, d_1
33. Circle(C, (0.2 * Distance[D, E])) → e_1
34. Intersect(e_1, b) → M,
35. Intersect(e_1, f) → N,
36. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], F) → A'_2
37. Dilate(F, If[5 < j ≤ 6, 6 - j, 0], E) → F'
38. Dilate(E, If[6 < j ≤ 7, 7 - j, 0], D) → E'
39. Rotate(E, If[7 < j ≤ 8, ((j - 7) * pi), 3.141592653589793], E) → E'_1
40. Rotate(E', If[7 < j ≤ 8, ((j - 7) * pi), 3.141592653589793], E) → E''
41. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], D) → C'_1
42. Vector(C, C'_1) → u
43. Angle(E, C, A) → β
44. CircleArc(A, C, A'') → s_1
45. Min({a', a, l}) → m
46. Circle(C, (0.4 * m)) → s
47. Intersect(s, l, 1) → Q
48. Intersect(s, a, 1) → R
49. Rotate(Q, If[0 < n ≤ 1, (n * β), β], C) → Q'
50. CircleSector(C, Q, Q') → t
51. Dilate(C, If[2 < n ≤ 3, 3 - n, 0], D) → C'_{2}
52. Vector(C, C'_{2}) → v
53. Translate(t, v) → t'
54. Rotate(t', If[2 < n ≤ 3, ((n - 2) * (pi - β)), pi - β], C'_{2}) → t''