交替外角：薄片任务3的几何构造与验证

GeoGebra 命令及参数

1. Point(y = 0) → A
2. Line(A, B) → f
3. Rotate(B, α, A) → B'
4. Angle(B, A, B') → γ
5. Line(A, B') → g
6. Rotate(B', β, A) → B''
7. Angle(B', A, B'') → δ
8. Line(A, B'') → h
9. Circle(A, a) → c
10. Intersect(c, h, 2) → C
11. Line(C, g) → i
12. Circle(C, A) → d
13. Circle(A, C) → e
14. Intersect(e, h, 2) → J
15. Segment(A, C) → j
16. Circle(A, (0.3 * j)) → k
17. Circle(C, (0.3 * j)) → p
18. Intersect(p, h) → N, O
19. Intersect(k, h) → P, Q
20. Intersect(k, g) → T, U
21. Intersect(p, i, 2) → V
22. Intersect(p, i, 1) → W
23. Circle(C, j / 2) → g_1
24. Circle(A, j / 2) → h_1
25. Intersect(g_1, i, 2) → D
26. Intersect(g_1, i, 1) → E
27. Intersect(g_1, h, 2) → H
28. Intersect(g_1, h) → I, Z
29. Intersect(h_1, h) → A_1, B_1
30. Intersect(h_1, g) → E_1, F_1
31. Point(j) → G_1
32. Vector(A, G_1) → u
33. Segment(A, G_1) → l
34. Ray(A, A_1) → m
35. Ray(C, H) → n
36. Vector(A, G_1) → v
37. Segment(G_1, C) → s
38. CircleArc(C, N, O) → r
39. Point(r) → F
40. Rotate(F, (-δ), C) → F'
41. Angle(F', C, F) → ε
42. Segment(A, C) → b
43. CircleSector(A, P, U) → d_1
44. Translate(d_1, v) → e_1
45. CircleArc(C, W, V) → f_1
46. Point(f_1) → G
47. Rotate(G, (-(pi - ε)), C) → G'
48. Angle(G', C, G) → ζ
49. CircleSector(C, G', G) → k_1
50. CircleArc(A, P, U) → q
51. Segment(A, C) → t